Spacetime quantum and classical mechanics with dynamical foliation Fecha: 2024-05-06Tipo de documento: ArticuloResumen:The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions. First, we promote the time choice of the Legendre transform to a dynamical variable. Second, we extend the Poisson brackets of matter fields to a spacetime symmetric form. The ensuing “spacetime phase space” is employed to obtain an explicitly covariant version of Hamilton equations for relativistic field theories. A canonical-like quantization of the formalism is then presented in which the fields satisfy spacetime commutation relations and the foliation is quantum. In this approach, the classical action is also promoted to an operator and retains explicit covariance through its nonseparability in the matter-foliation partition. The problem of establishing a correspondence between the new noncausal framework (where fields at different times are independent) and conventional QM is solved through a generalization of spacelike correlators to spacetime. In this generalization, the Hamiltonian is replaced by the action, and conventional particles by off-shell particles. When the foliation is quantized, the previous map is recovered by conditioning on foliation eigenstates, in analogy with the Page and Wootters mechanism. We also provide an interpretation of the correspondence in which the causal structure of a given theory emerges from the quantum correlations between the system and an environment. This idea holds for general quantum systems and allows one to generalize the density matrix to an operator containing the information of correlators both in space and time.Compartir:
Modalidad de enseñanza en la post-pandemia: reflexiones en base a opiniones de estudiantes y docentes de un curso de Matemática en la Facultad de Ingeniería Fecha: 2022-01-01Tipo de documento: Objeto de conferenciaResumen:Este trabajo es realizado por integrantes de la UIDET IMApEC en el marco del proyecto de investigación “Articulación en la enseñanza en Ciencias Básicas en las carreras de Ingeniería”. Se reflexiona sobre los posibles escenarios de modalidades de cursada para la Cátedra de Matemática C (Ciclo Básico) de la Facultad de Ingeniería de la Universidad Nacional de la Plata (FI-UNLP) en la post-pandemia. Se presentan resultados de un cuestionario a docentes y estudiantes de tal asignatura y los resultados académicos de dos años anteriores a la pandemia y los dos años de dictado en modalidad virtual.Compartir:
Many-body entanglement in fermion systems Fecha: 2021-05-20Tipo de documento: ArticuloResumen:We discuss a general bipartitelike representation and Schmidt decomposition of an arbitrary pure state of N indistinguishable fermions, based on states of M < N and ( N − M ) fermions. It is directly connected with the reduced M - and ( N − M ) -body density matrices (DMs), which have the same spectrum in such states. The concept of M -body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized M -body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as postmeasurement states. Moreover, such entropy is an upper bound to the bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of M and N − M effectively distinguishable fermions. Analytic evaluation of the spectrum of M -body DMs in some strongly correlated fermionic states is also provided.Compartir:
Modalidad de enseñanza en la post-pandemia: Opiniones de estudiantes y docentes de un curso de matemática Fecha: 2021-01-01Tipo de documento: Objeto de conferenciaResumen:Este trabajo es realizado por integrantes de la UIDET IMApEC en el marco del proyecto de investigación “Articulación en la enseñanza en Ciencias Básicas en las carreras de Ingeniería”. Se intenta reflexionar sobre los posibles escenarios de modalidades de cursada para la Cátedra de Matemática C (Ciclo Básico) de la Facultad de Ingeniería de la Universidad Nacional de la Plata (FI-UNLP) cuando se llegue a un periodo de post-pandemia.Compartir:
Space-time quantum actions Fecha: 2021-01-01Tipo de documento: PreprintResumen:We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum generalization of the corresponding classical action. The diagonalization of such quantum actions enables us to recover the predictions of conventional quantum mechanics and reveals an extended unitary equivalence between all physical theories. Quantum correlations and coherent effects across time and between distinct theories acquire a rigorous meaning, which is encoded in the rich temporal structure of physical states. Connections with modern relativistic schemes and the path integral formulation also emerge.Compartir:
One-body entanglement as a quantum resource in fermionic systems Fecha: 2020-10-01Tipo de documento: ArticuloResumen:We show that one-body entanglement, which is a measure of the deviation of a pure fermionic state from a Slater determinant (SD) and is determined by the mixedness of the single-particle density matrix (SPDM), can be considered as a quantum resource. The associated theory has SDs and their convex hull as free states, and number conserving fermion linear optics operations (FLO), which include one-body unitary transformations and measurements of the occupancy of single-particle modes, as the basic free operations. We first provide a bipartitelike formulation of one-body entanglement, based on a Schmidt-like decomposition of a pure N-fermion state, from which the SPDM [together with the (N-1)-body density matrix] can be derived. It is then proved that under FLO operations the initial and postmeasurement SPDMs always satisfy a majorization relation, which ensures that these operations cannot increase, on average, the one-body entanglement. It is finally shown that this resource is consistent with a model of fermionic quantum computation which requires correlations beyond antisymmetrization. More general free measurements and the relation with mode entanglement are also discussed.Compartir:
Separability and parity transitions in XYZ spin systems under nonuniform fields Fecha: 2020-05-05Tipo de documento: ArticuloResumen:We examine the existence of completely separable ground states (GS) in finite spin-s arrays with anisotropic XYZ couplings, immersed in a nonuniform magnetic field along one of the principal axes. The general conditions for their existence are determined. The analytic expressions for the separability curve in field space, and for the ensuing factorized state and GS energy, are then derived for alternating solutions, valid for any spin and size. They generalize results for uniform fields and show that nonuniform fields can induce GS factorization also in systems which do not exhibit this phenomenon in a uniform field. It is also shown that such a curve corresponds to a fundamental Sz-parity transition of the GS, present for any spin and size, and that two different types of GS parity diagrams can emerge, according to the anisotropy. The role of factorization in the magnetization and entanglement of these systems is also analyzed, and analytic expressions at the borders of the factorizing curve are provided. Illustrative examples for spin pairs and chains are as well discussed.Compartir:
Conditional states and entropy in qudit-qubit systems Fecha: 2019-06-25Tipo de documento: ArticuloResumen:We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit the conditional postmeasurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of postmeasurement qubit states can form more complex solid regions. In particular, we show the emergence, for some classes of mixed states, of sets which are the convex hull of solid ellipsoids and which may lead to conelike and trianglelike shapes in limit cases. We also analyze the associated measurement-dependent conditional entropy, providing a full analytic determination of its minimum and of the minimizing local measurement at the qudit for the previous states. Separable rank-2 mixtures are also discussed.Compartir:
Parallel-in-time optical simulation of history states Autores:Pabón, D. Rebón, Lorena Bordakevich, S. Gigena, Nicolás Alejandro Boette, Alan Pablo Iemmi, Claudio Rossignoli, Raúl Dante Ledesma, Silvia Fecha: 2019-06-25Tipo de documento: ArticuloResumen:We present an experimental optical implementation of a parallel-in-time discrete model of quantum evolution, based on the entanglement between the quantum system and a finite-dimensional quantum clock. The setup is based on a programmable spatial light modulator which entangles the polarization and transverse spatial degrees of freedom of a single photon. It enables the simulation of a qubit history state containing the whole evolution of the system, capturing its main features in a simple and configurable scheme. We experimentally determine the associated system-time entanglement, which is a measure of distinguishable quantum evolution, and also the time average of observables, which in the present realization can be obtained through one single measurement.Compartir:
Inducing critical phenomena in spin chains through sparse alternating fields Autores:Cerezo de la Roca, Marco Vinicio Sebastián Rossignoli, Raúl Dante Canosa, Norma Beatriz Lamas, Carlos Alberto Fecha: 2019-01-01Tipo de documento: ArticuloResumen:We analyze the phase diagram of the exact ground state (GS) of spin-s chains with ferromagnetic XXZ couplings under n-alternating field configurations, i.e, sparse alternating fields having nodes at n−1 contiguous sites. It is shown that such systems can exhibit a non-trivial magnetic behavior, which can differ significantly from that of the standard (n = 1) alternating case and enable mechanisms for controlling their magnetic and entanglement properties. The boundary in field space of the fully aligned phase can be determined analytically ∀ n, and shows that it becomes reachable only above a threshold value of the coupling anisotropy Jz/J, which depends on n but is independent of the system size. Below this value the maximum attainable magnetization becomes much smaller. We then show that the GS can exhibit significant magnetization plateaus, persistent for large systems, at which the magnetization per site m obeys the quantization rule 2n(s −m) = integer, consistent with the Oshikawa, Yamanaka and Affleck (OYA) criterion. We also identify the emergence of field induced spin polymerization, which explains the presence of such plateaus. Entanglement and field induced frustration effects are also analyzed.Compartir:
Análisis de un proceso educativo mediante cartas de control: el caso de un curso de matemática universitaria Fecha: 2019-01-01Tipo de documento: ResumenResumen:En la mayor parte de los centros de producción de importancia se aplica la técnica estadística conocida con el nombre de control estadístico de procesos (CEP), con el objeto de realizar un monitoreo de la producción, mantener un nivel adecuado de calidad de los productos fabricados, controlar la estabilidad y la capacidad de la misma. Entre las herramientas empleadas en el CEP, se encuentran las denominadas Cartas de Control (CC), mediante las cuales se puede realizar el monitoreo de variables de importancia en el desarrollo de un proceso en el tiempo. Estas permiten realizar una detección temprana de la desviación de los valores de la variable monitoreada respecto a un valor y límites determinados a priori, y de esta manera se podrían detectar cambios e identificar las posibles causales asignables a los mismos. En el caso de un proceso educativo, que se ve afectado por múltiples factores, externos e internos a la institución, el CEP y las CC se convierten en una herramienta útil para conseguir la estabilidad o mejora de la calidad educativa mediante el seguimiento en el tiempo de algunas variables o atributos como pueden ser el rendimiento académico, el tránsito de los estudiantes en las carreras y la cantidad de egresos, en una institución (Salazar, Cañón, 2011). En esta línea en el presente trabajo se propone analizar con esas herramientas estadísticas el proceso educativo correspondiente a la evolución temporal durante 23 semestres (desde el año 2006 al 2017) de cursos de Matemática C, que estuvieron a cargo de un mismo profesor, del Área de Ciencias Básicas de la Facultad de Ingeniería de la Universidad Nacional de La Plata. Se analizan mediante CC la variabilidad de algunas proporciones de algunas cantidades en el tiempo. También se relevan los posibles factores a los que podrían atribuirse cambios u anomalías encontradas. Los resultados obtenidos muestran un proceso bajo control, salvo algunas anomalías y una variabilidad en el proceso, en especial una reducción en la media de la proporción de cantidad de alumnos que abandonan en relación con la cantidad de inscriptos. Esto sería atribuido a cambios, que ha ido implementado el profesor a cargo, que se vinculan con los distintos modos de evaluar los rendimientos académicos de los estudiantes en los cursos registrados.Compartir:
Correlaciones e información cuántica con fotones Autores:Rebón, Lorena Boette, Alan Pablo Gigena, Nicolás Alejandro Rossignoli, Raúl Dante Roig, Alejandro Ramón Fecha: 2019-01-01Tipo de documento: ResumenResumen:En un principio, la Teoría de la Información fue concebida en forma abstracta, en base a una formulación matemática. Sin embargo, la habilidad y eficiencia para procesar o transmitir información dependerá en última instancia del sistema físico elegido para codificar esa información. Es así que, al codificar la información en las propiedades físicas de sistemas cuyo comportamiento se describe por las leyes de la mecánica cuántica, se abren nuevas posibilidades que son irrealizables clásicamente. Entre ellas, la posibilidad de generar algoritmos cuánticos para ciertos cálculos que requieren un número de pasos significativamente menor que cualquier algoritmo clásico, reduciendo su complejidad, o mantener comunicaciones seguras sin importar las capacidades tecnológicas de un potencial espía. Entre las características fundamentales de la mecánica cuántica que posibilitan estos desarrollos, sobresalen el principio de superposición y el entrelazamiento cuántico, el cual denota un tipo de correlaciones, sin análogo clásico, que pueden exhibir los sistemas cuánticos compuestos. Una de las implementaciones más accesibles para la comunicación cuántica y el procesamiento cuántico de la información emplea fotones individuales como portadores de la información. Estos pueden viajar entre dos estaciones distantes siendo poco afectados por el ruido que introduce el entorno. Además, poseen varios grados de libertad en los cuales es posible codificar la información y pueden manipularse con un alto grado de control utilizando tecnología estándar. En este trabajo se describen algunas aplicaciones de la implementación fotónica, realizadas en colaboración con el Laboratorio de Procesado de Imágenes (LPI) del Depto. de Física de la UBA. En primer lugar, se describe la determinación experimental de medidas de correlaciones cuánticas en estados no puros de un par de fotones correlacionados en polarización, mediante técnicas de tomografía de estados cuánticos. Luego se describe la utilización de moduladores espaciales de luz programables para entrelazar la polarización con grados de libertad espaciales, y así poder simular los denominados estados historia de evoluciones temporales cuánticas. Se muestra que este último es un esquema eficientemente para el cálculo de promedios temporales de los observables del sistema.Compartir:
History state formalism for Dirac’s theory Fecha: 2019-01-01Tipo de documento: PreprintResumen:We propose a history state formalism for a Dirac particle. By introducing a reference quantum clock system it is first shown that Dirac's equation can be derived by enforcing a timeless Wheeler-DeWitt-like equation for a global state. The Hilbert space of the whole system constitutes a unitary representation of the Lorentz group with respect to a properly defined invariant product, and the proper normalization of global states directly ensures standard Dirac's norm. Moreover, by introducing a second quantum clock, the previous invariant product emerges naturally from a generalized continuity equation. The invariant parameter τ associated with this second clock labels history states for different particles, yielding an observable evolution in the case of a hypothetical superposition of different masses. Analytical expressions for both the space-time density and electron-time entanglement are provided for two particular families of electron states, the former including Pryce localized particles.Compartir:
History state formalism for scalar particles Fecha: 2019-01-01Tipo de documento: ArticuloResumen:We present a covariant quantum formalism for scalar particles based on an enlarged Hilbert space. The particular physical theory can be introduced through a timeless Wheeler DeWitt-like equation, whose projection onto four-dimensional coordinates leads to the Klein-Gordon equation. The standard quantum mechanical product in the enlarged space, which is invariant and positive definite, implies the usual Klein-Gordon product when applied to its eigenstates. Moreover, the standard three-dimensional invariant measure emerges naturally from the flat measure in four dimensions when mass eigenstates are considered, allowing a rigorous identification between definite mass history states and the standard Wigner representation. Connections with the free propagator of scalar field theory and localized states are subsequently derived. The formalism also allows the superposition of different theories and remains valid in the presence of a fixed external field, revealing special orthogonality relations. Other details such as extended identities for the current density, the quantization of parameterized theories and the nonrelativistic limit, with its connection to the Page and Wooters formalism, are discussed. A related consistent second quantization formulation is also introduced.Compartir:
Fermionic entanglement in the Lipkin model Fecha: 2019-01-01Tipo de documento: PreprintResumen:We examine the fermionic entanglement in the ground state of the fermionic Lipkin model and its relation with bipartite entanglement. It is first shown that the one-body entanglement entropy, which quantifies the minimum distance to a fermionic Gaussian state, behaves similarly to the mean-field order parameter and is essentially proportional to the total bipartite entanglement between the upper and lower modes, a quantity meaningful only in the fermionic realization of the model. We also analyze the entanglement of the reduced state of four single-particle modes (two up-down pairs), showing that its fermionic concurrence is strongly peaked at the phase transition and behaves differently from the corresponding up-down entanglement. We finally show that the first measures and the up-down reduced entanglement can be correctly described through a basic mean-field approach supplemented with symmetry restoration, whereas the concurrence requires at least the inclusion of random-phase-approximation--type correlations for a proper prediction. Fermionic separability is also discussed.Compartir:
Computación cuántica: ¿el futuro de los procesadores? Autores:Rossignoli, Raúl Fecha: 2018-12-01Tipo de documento: ArticuloResumen:La computación cuántica es una nueva forma de representar y procesar la información, basada expresamente en las leyes de la mecánica cuántica. A diferencia de la computación clásica, se basa en qubits (quantum bits), que pueden estar no sólo en dos estados dados, digamos 0 y 1, sino también en cualquier superposición de ellos, de acuerdo a uno de los principios básicos de la mecánica cuántica.Compartir:
Fermionic entanglement in superconducting systems Fecha: 2018-01-01Tipo de documento: ArticuloResumen:We examine distinct measures of fermionic entanglement in the exact ground state of a finite superconducting system. It is first shown that global measures such as the one-body entanglement entropy, which represents the minimum relative entropy between the exact ground state and the set of fermionic Gaussian states, exhibit a close correlation with the BCS gap, saturating in the strong superconducting regime. The same behavior is displayed by the bipartite entanglement between the set of all single-particle states k of positive quasimomenta and their time-reversed partners k̄. In contrast, the entanglement associated with the reduced density matrix of four single-particle modes k,k̄, k′,k̄′, which can be measured through a properly defined fermionic concurrence, exhibits a different behavior, showing a peak in the vicinity of the superconducting transition for states k,k′ close to the Fermi level and becoming small in the strong coupling regime. In the latter, such reduced state exhibits, instead, a finite mutual information and quantum discord. While the first measures can be correctly estimated with the BCS approximation, the previous four-level concurrence lies strictly beyond the latter, requiring at least a particle-number projected BCS treatment for its description. Formal properties of all previous entanglement measures are as well discussed.Compartir:
Álgebra Lineal con aplicaciones: Parte I Autores:Rossignoli, Raúl Fecha: 2018-01-01Tipo de documento: LibroResumen:Este libro está pensado como texto para ser utilizado en la parte inicial de un curso, de duración semestral, sobre Álgebra Lineal para carreras de Ingeniería y otras Ciencias Aplicadas. El libro está basado en las guías teórico-prácticas elaboradas inicialmente por la que fuera Profesora Titular de la asignatura Matemática C de la Facultad de Ingeniería de la UNLP, Lic. Nélida Echebest. Esta base fue luego reelaborada y enriquecida con aportes de los presentes autores, profesores de dicha asignatura, teniendo como referencia la bibliografía indicada al final del presente libro. Dicha asignatura, correspondiente al tercer trimestre de las carreras de Ingeniería de la Universidad Nacional de La Plata, introduce herramientas básicas que son de utilidad en la modelización y resolución de problemas de Ingeniería, Física, Química, etc. Por esta misma razón, el presente libro puede resultar también útil para cursos destinados a estudiantes de otras disciplinas científicas. Se ha dado por supuesto que el lector ha adquirido, previamente, una formación básica sobre Análisis Matemático en una y varias variables reales. El libro contiene desarrollos teóricos, incluyendo las principales demostraciones, y además numerosos ejemplos resueltos en detalle, junto con interpretaciones geométricas y fi guras, para reforzar y clari ficar los conceptos introducidos. Asimismo, se presenta una amplia variedad de problemas y aplicaciones.Compartir:
Complexity of a matter-field Hamiltonian in the vicinity of a quantum instability Fecha: 2018-01-01Tipo de documento: ArticuloResumen:Using as information-quantifiers the entropy and the statistical complexity, we analyze the rich, complex dynamics of a special non linear Hamiltonian H. H describes the interaction between a quantum system and a classical one. The concomitant system exhibits periodicity, quasi-periodicity, not-boundedness, and chaotic regimes. The chaotic phenomenon, together with complex dynamics, arise in the vicinity of an unstable case, that of the purely quantum system.2) Complexity of a matter-field Hamiltonian in the vicinity of aquantum instability.Compartir:
History states of systems and operators Autores:Boette, Alan Pablo Rossignoli, Raúl Fecha: 2018-01-01Tipo de documento: ArticuloResumen:We discuss some fundamental properties of discrete system-time history states. Such states arise for a quantum reference clock of finite dimension and lead to a unitary evolution of system states when satisfying a static discrete Wheeler-DeWitt-type equation. We consider the general case where system-clock pairs can interact, analyzing first their different representations and showing there is always a special clock basis for which the evolution for a given initial state can be described by a constant Hamiltonian H. It is also shown, however, that when the evolution operators form a complete orthogonal set, the history state is maximally entangled for any initial state, as opposed to the case of a constant H, and can be generated through a simple double-clock setting. We then examine the quadratic system-time entanglement entropy, providing an analytic evaluation and showing it satisfies strict upper and lower bounds determined by the energy spread and the geodesic evolution connecting the initial and final states. We finally show that the unitary operator that generates the history state can itself be considered as an operator history state, whose quadratic entanglement entropy determines its entangling power. Simple measurements on the clock enable one to efficiently determine overlaps between system states and also evolution operators at any two times.Compartir:
Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes Fecha: 2018-01-01Tipo de documento: ArticuloResumen:We examine the emergence of chaos in a non-linear model derived from a semiquantum Hamiltonian describing the coupling between a classical field and a quantum system. The latter corresponds to a bosonic version of a BCS-like Hamiltonian, and possesses stable and unstable regimes. The dynamics of the whole system is shown to be strongly influenced by the quantum subsystem. In particular, chaos is seen to arise in the vicinity of a quantum critical case, which separates the stable and unstable regimes of the bosonic system.Compartir:
Bipartite entanglement in fermion systems Fecha: 2017-06-01Tipo de documento: ArticuloResumen:We discuss the relation between fermion entanglement and bipartite entanglement. We first show that an exact correspondence between them arises when the states are constrained to have a definite local number parity. Moreover, for arbitrary states in a four dimensional single-particle Hilbert space, the fermion entanglement is shown to measure the entanglement between two distinguishable qubits defined by a suitable partition of this space. Such entanglement can be used as a resource for tasks like quantum teleportation. On the other hand, this fermionic entanglement provides a lower bound to the entanglement of an arbitrary bipartition although in this case the local states involved will generally have different number parities. Finally the fermionic implementation of the teleportation and superdense coding protocols based on qubits with odd and even number parity is discussed, together with the role of the previous types of entanglement.Compartir:
Enseñanza del álgebra lineal en una facultad de Ingeniería: Aspectos metodológicos y didácticos Autores:Costa, Viviana Angélica Rossignoli, Raúl Fecha: 2017-01-01Tipo de documento: ArticuloResumen:En este trabajo describimos el enfoque con que se enseñan los conceptos relativos al Algebra Lineal en una asignatura del Área de Ciencias Básicas en una Facultad de Ingeniería de la República Argentina. Además exponemos los resultados de un cuestionario realizado a sus estudiantes que tiene el propósito de identificar las causas de los posibles obstáculos en la enseñanza y aprendizaje de esos conceptos, y que contiene también información sobre otros aspectos del curso. Se observa un acuerdo de los estudiantes con la metodología empleada, junto con algunas dificultades en el aprendizaje de ciertos temas y en comprender su vinculación con la Ingeniería. El mismo serviría de base para implementar estrategias didácticas o cambios metodológicos que reviertan las mismas, como así también el de brindar aportes que sirvan de referencia para dar iniciativa a posteriores investigaciones. In this paper we describe the approach employed to teach the basic concepts related to linear algebra in a course of the Area of Basic Sciences in an Engineering Faculty of Argentina. Besides, we present the results of a questionnaire made for these students that aims to identify the origins of possible obstacles in the teaching and learning of these concepts, and which also contains information about other aspects of the course. An agreement of the students with the methodology employed is observed, together with some difficulties in the learning of particular topics and in understanding their connection with Engineering. This survey could be used to implement teaching strategies and//or methodological changes that may reverse the previous obstacles, as well as to provide input for further research initiatives.Compartir:
Entanglement and coherence in a spin-s XXZ system under non-uniform fields Fecha: 2017-01-01Tipo de documento: ArticuloResumen:We investigate entanglement and coherence in an XXZ spin-s pair immersed in a non-uniform transverse magnetic field. The ground state and thermal entanglement phase diagrams are analyzed in detail in both the ferromagnetic and antiferromagnetic cases. It is shown that a non-uniform field enables to control the energy levels and the entanglement of the corresponding eigenstates, making it possible to entangle the system for any value of the exchange couplings, both at zero and finite temperatures. Moreover, the limit temperature for entanglement is shown to depend only on the difference |h1 − h2| between the fields applied at each spin, leading for T > 0 to a separability stripe in the (h1, h2) field plane such that the system becomes entangled above a threshold value of |h1 − h2|. These results are demonstrated to be rigorously valid for any spin s. On the other hand, the relative entropy of coherence in the standard basis, which coincides with the ground state entanglement entropy at T = 0 for any s, becomes non-zero for any value of the fields at T > 0, decreasing uniformly for sufficiently high T . A special critical point arising at T = 0 for nonuniform fields in the ferromagnetic case is also discussed.Compartir:
Spectrum and normal modes of non-hermitian quadratic boson operators Autores:García, Javier Rossignoli, Raúl Fecha: 2017-01-01Tipo de documento: PreprintResumen:We analyze the spectrum and normal mode representation of general quadratic bosonic formsHnot necessarily hermitian. It is shown that in the one-dimensional case such forms exhibit either an harmonic regime where bothHandH^†have a discrete spectrum with biorthogonal eigenstates, and a coherent-like regime where eitherHorH†have a continuous complex two-fold degenerate spectrum, while its adjoint has no convergent eigenstates. These regimes reflect the nature of the pertinent normal boson operators. Non-diagonalizable cases as well critical boundary sectors separating these regimes are also analyzed. The extension toN-dimensional quadratic systems is as well discussed.Compartir:
Quantum discord and entropic measures of quantum correlations: Optimization and behavior in finite XY spin chains Autores:Canosa, Norma Beatriz Cerezo de la Roca, Marco Vinicio Sebastián Gigena, Nicolás Alejandro Rossignoli, Raúl Dante Fernandes Fanchini, Felipe Oliveira Soares Pinto, Diogo Adesso, Gerardo Fecha: 2017-01-01Tipo de documento: Capitulo de libroResumen:We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finiteXYspin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behavior, their optimizing measurements exhibit significant differences, which can be understood and predicted through the previous approximations. The remarkable behavior of these quantities in the vicinity of transverse and non-transverse factorizing fields is also discussed.Compartir:
Factorization and criticality in finite XXZ systems of arbitrary spin Autores:Cerezo de la Roca, Marco Vinicio Sebastián Rossignoli, Raúl Dante Canosa, Norma Beatriz Rios, E. Fecha: 2017-01-01Tipo de documento: ArticuloResumen:We analyze ground state (GS) factorization in general arrays of spinss_iwithXXZcouplings immersed in nonuniform fields. It is shown that an exceptionally degenerate set of completely separable symmetry-breaking GS's can arise for a wide range of field configurations, at a quantum critical point where all GS magnetization plateaus merge. Such configurations include alternating fields as well as zero bulk field solutions with edge fields only and intermediate solutions with zero field at specific sites, valid ford-dimensional arrays. The definite magnetization projected GS's at factorization can be analytically determined and depend only on the exchange anisotropies, exhibiting critical entanglement properties. We also show that some factorization compatible field configurations may result in field-induced frustration and nontrivial behavior at strong fields.Compartir:
Pair entanglement in dimerized spin-<i>s</i> chains Fecha: 2016-12-01Tipo de documento: ArticuloResumen:We examine the pair entanglement in the ground state of finite dimerized spin-s chains interacting through anisotropic XY couplings immersed in a transverse magnetic field by means of a self-consistent pair mean-field approximation. The approach, which makes no a priori assumptions on the pair states, predicts, for sufficiently low coupling between pairs, 2s distinct dimerized phases for increasing fields below the pair factorizing field, separated by spin-parity-breaking phases. The dimerized phases lead to approximate magnetization and pair entanglement plateaus, while the parity-breaking phases are characterized by weak pair entanglement but non-negligible entanglement of the pair with the rest of the system. These predictions are confirmed by the exact results obtained in finite s=1 and s=3/2 chains. It is also shown that for increasing values of the spin s, the entanglement of an isolated pair, as measured by the negativity, rapidly saturates in the anisotropic XY case but increases as s1/2 in the XX case, reflecting a distinct single-spin entanglement spectrum.Compartir:
Factorization in spin systems under general fields and separable ground-state engineering Fecha: 2016-10-01Tipo de documento: ArticuloResumen:We discuss ground-state factorization schemes in spin S arrays with general quadratic couplings under general magnetic fields, not necessarily uniform or transverse. It is shown that, given arbitrary spin alignment directions at each site, nonzero XYZ couplings between any pair and fields at each site always exist such that the ensuing Hamiltonian has an exactly separable eigenstate with the spins pointing along the specified directions. Furthermore, by suitable tuning of the fields this eigenstate can always be cooled down to a nondegenerate ground state. It is also shown that in open one-dimensional systems with fixed arbitrary first-neighbor couplings at least one separable eigenstate compatible with an arbitrarily chosen spin direction at one site is always feasible if the fields at each site can be tuned. We demonstrate as well that in the vicinity of factorization, i.e., for small perturbations in the fields or couplings, pairwise entanglement reaches full range. Some noticeable examples of factorized eigenstates are unveiled. The present results open the way for separable ground-state engineering. A notation to quantify the complexity of a given type of solution according to the required control on the system couplings and fields is introduced.Compartir:
Conditional purity and quantum correlation measures in two qubit mixed states Autores:Rebón, Lorena Rossignoli, Raúl Dante Varga, Juan José Miguel Gigena, Nicolás Alejandro Canosa, Norma Beatriz Iemmi, Claudio César Ledesma, Silvia Adriana Fecha: 2016-09-01Tipo de documento: PreprintResumen:We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.Compartir:
One-body information loss in fermion systems Fecha: 2016-01-01Tipo de documento: ArticuloResumen:We propose an entropic measure of nonclassical correlations in general mixed states of fermion systems, based on the loss of information due to the unread measurement of the occupancy of single-particle states of a given basis. When minimized over all possible single-particle bases, the measure reduces to an entanglement entropy for pure states and vanishes only for states which are diagonal in a Slater determinant basis. The approach is also suitable for states having definite number parity yet not necessarily a fixed particle number, in which case the minimization can be extended to all bases related through a Bogoliubov transformation if quasiparticle mode measurements are also considered. General stationary conditions for determining the optimizing basis are derived. For a mixture of a general pure state with the maximally mixed state, a general analytic evaluation of the present measure and optimizing basis is provided, which shows that nonentangled mixed states may nonetheless exhibit a nonzero information loss.Compartir:
System-time entanglement in a discrete time model Autores:Boette, Alan Pablo Rossignoli, Raúl Dante Gigena, Nicolás Alejandro Cerezo de la Roca, Marco Vinicio Sebastián Fecha: 2016-01-01Tipo de documento: PreprintResumen:We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is able to represent the evolution over2ntime steps in terms of justntime qubits andncontrol gates. We then introduce the concept of system-time entanglement as a measure of distinguishable quantum evolution, based on the entanglement between the system and the reference clock. This quantity vanishes for stationary states and is maximum for systems jumping onto a new orthogonal state at each time step. In the case of a constant Hamiltonian leading to a cyclic evolution it is a measure of the spread over distinct energy eigenstates, and satisfies an entropic energy-time uncertainty relation. The evolution of mixed states is also examined. Analytical expressions for the basic case of a qubit clock, as well as for the continuous limit in the evolution between two states, are provided.Compartir:
Exact dynamics and squeezing in two harmonic modes coupled through angular momentum Fecha: 2015-01-01Tipo de documento: ArticuloResumen:We investigate the exact dynamics of a system of two independent harmonic oscillators coupled through their angular momentum. The exact analytic solution of the equations of motion for the field operators is derived, and the conditions for dynamical stability are obtained. As application, we examine the emergence of squeezing and mode entanglement for an arbitrary separable coherent initial state. It is shown that close to instability, the system develops considerable entanglement, which is accompanied with simultaneous squeezing in the coordinate of one oscillator and the momentum of the other oscillator. In contrast, for weak coupling away from instability, the generated entanglement is small, with weak alternating squeezing in the coordinate and momentum of each oscillator. Approximate expressions describing these regimes are also provided.Compartir:
Nontransverse factorizing fields and entanglement in finite spin systems Fecha: 2015-01-01Tipo de documento: ArticuloResumen:We determine the conditions for the existence of nontransverse factorizing magnetic fields in general spin arrays with anisotropic XYZ couplings of arbitrary range. It is first shown that a uniform, maximally aligned, completely separable eigenstate can exist just for fields hs parallel to a principal plane and forming four straight lines in the field space, with the alignment direction different from that of hs and determined by the anisotropy. Such a state always becomes a nondegenerate ground state for sufficiently strong (yet finite) fields along these lines, in both ferromagnetic and antiferromagnetic-type systems. In antiferromagnetic chains, this field coexists with the nontransverse factorizing field h i s associated with a degenerate N´eel-type separable ground state, which is shown to arise at a level crossing in a finite chain. It is also demonstrated for arbitrary spin that pairwise entanglement reaches full range in the vicinity of both hs and h i s , vanishing at hs but approaching small yet finite side limits at h i s , which are analytically determined. The behavior of the block entropy and entanglement spectrum in their vicinity is also analyzed.Compartir:
Generalized mean-field description of entanglement in dimerized spin systems Fecha: 2015-01-01Tipo de documento: ArticuloResumen:We discuss a generalized self-consistent mean-field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin-1/2 systems with anisotropic ferromagnetic-type XY and XYZ couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single-spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration. the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.Compartir:
Non-transverse factorizing fields and entanglement in finite spin systems Fecha: 2015-01-01Tipo de documento: ArticuloResumen:We determine the conditions for the existence of non-transverse factorizing magnetic fields in general spin arrays with anisotropic XY Z couplings of arbitrary range. It is first shown that a uniform maximally aligned completely separable eigenstate can exist just for fields hs parallel to a principal plane and forming four straight lines in field space, with the alignment direction different from that of hs and determined by the anisotropy. Such state always becomes a non-degenerate ground state (GS) for sufficiently strong (yet finite) fields along these lines, in both ferromagnetic (FM) and antiferromagnetic (AFM) type systems. In AFM chains, this field coexists with the nontransverse factorizing field h′ s associated with a degenerate N´eel-type separable GS, which is shown to arise at a level crossing in a finite chain. It is also demonstrated for arbitrary spin that pairwise entanglement reaches full range in the vicinity of both hs and h′ s, vanishing at hs but approaching small yet finite side-limits at h′ s, which are analytically determined. The behavior of the block entropy and entanglement spectrum in their vicinity is also analyzed.Compartir:
Quantum Discord and Information Deficit in Spin Chains Fecha: 2015-01-01Tipo de documento: ArticuloResumen:We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one-way information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All of these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.Compartir:
Entanglement in fermion systems Fecha: 2015-01-01Tipo de documento: ArticuloResumen:We analyze the problem of quantifying entanglement in pure and mixed states of fermionic systems with fixed number parity yet not necessarily fixed particle number. The mode entanglement between one single-particle level and its orthogonal complement is first considered, and an entanglement entropy for such a partition of a particular basis of the single-particle Hilbert spaceHis defined. The sum over all single-particle modes of this entropy is introduced as a measure of the total entanglement of the system with respect to the chosen basis and it is shown that its minimum over all bases ofHis a function of the one-body density matrix. Furthermore, we show that if minimization is extended to all bases related through a Bogoliubov transformation, then the entanglement entropy is a function of the generalized one-body density matrix. These results are then used to quantify entanglement in fermion systems with four single-particle levels. For general pure states of such a system a closed expression for the fermionic concurrence is derived, which generalizes the Slater correlation measure defined in [J. Schliemann et al, Phys. Rev. A 64, 022303 (2001)], implying that particle entanglement may be seen as minimum mode entanglement . It is also shown that the entanglement entropy defined before is related to this concurrence by an expression analogous to that of the two-qubit case. For mixed states of this system the convex roof extension of the previous concurrence and entanglement entropy are evaluated analytically, extending the results of previous ref. to general states.Compartir:
Generalized conditional entropy optimization for qudit-qubit states Fecha: 2014-10-16Tipo de documento: ArticuloResumen:We derive a general approximate solution to the problem of minimizing the conditional entropy of a qudit-qubit system resulting from a local measurement on the qubit, which is valid for general entropic forms and becomes exact in the limit of weak correlations. This entropy measures the average conditional mixedness of the postmeasurement state of the qudit, and its minimum among all local measurements represents a generalized entanglement of formation. In the case of the von Neumann entropy, it is directly related to the quantum discord. It is shown that at the lowest nontrivial order, the problem reduces to the minimization of a quadratic form determined by the correlation tensor of the system, the Bloch vector of the qubit and the local concavity of the entropy, requiring just the diagonalization of a 3×3 matrix. A simple geometrical picture in terms of an associated correlation ellipsoid is also derived, which illustrates the link between entropy optimization and correlation access and which is exact for a quadratic entropy. The approach enables a simple estimation of the quantum discord. Illustrative results for two-qubit states are discussed.Compartir:
Ecuaciones diferenciales en Física Fecha: 2014-01-01Tipo de documento: LibroResumen:Como su título lo indica, este libro está pensado como texto básico para un primer curso, de duración semestral, sobre Ecuaciones Diferenciales. Aunque algunos de sus contenidos se han tomado de las referencias, contiene numerosos aportes propios. En efecto, está basado en los apuntes de clase que los autores elaboramos durante los diversos períodos en que tuvimos a cargo la asignatura Matemáticas Especiales II, correspondiente al tercer año de la carrera de Licenciatura en Física de la Universidad Nacional de La Plata. Por consiguiente, pone énfasis en aquellos aspectos que son de utilidad en la modelización y resolución de problemas que plantea dicha disciplina científica. Por esta razón, entendemos que puede resultar igualmente útil para cursos destinados a alumnos/as de otras disciplinas directamente relacionadas con la Física, como la Ingeniería, las Ciencias Astronómicas y Geofísicas. Al escribirlo, hemos dado por descontado que su lector/a ha adquirido, previamente, una formación básica sobre Análisis Matemático en una y varias variables reales y en variable compleja, así como sobre Álgebra y Álgebra Lineal. Convencidos de que no se puede comprender profundamente la Física sin abordar seriamente el estudio de su principal herramienta, la Matemática, hemos cuidado al máximo la rigurosidad. Por esa causa, damos la demostración de cada aseveración que la requiere, con la sola excepción de aquellos temas que corresponden a los contenidos de asignaturas previas de Matemática o que se demuestran más naturalmente con herramientas que se obtendrán en cursos posteriores. (Párrafo extraído del texto a modo de resumen)Compartir:
Dynamics of entanglement between two harmonic modes in stable and unstable regimes Fecha: 2014-01-01Tipo de documento: ArticuloResumen:The exact dynamics of the entanglement between two harmonic modes generated by an angular momentum coupling is examined. Such system arises when considering a particle in a rotating anisotropic harmonic trap or a charged particle in a fixed harmonic potential in a magnetic field, and exhibits a rich dynamical structure, with stable, unstable and critical regimes according to the values of the rotational frequency or field and trap parameters. Consequently, it is shown that the entanglement generated from an initially separable gaussian state can exhibit quite distinct evolutions, ranging from quasiperiodic behavior in stable sectors to different types of unbounded increase in critical and unstable regions. The latter lead respectively to a logarithmic and linear growth of the entanglement entropy with time. It is also shown that entanglement can be controlled by tuning the frequency, such that it can be increased, kept constant or returned to a vanishing value just with stepwise frequency variations. Exact asymptotic expressions for the entanglement entropy in the different dynamical regimes are provided.Compartir:
Discord and information deficit in the XX chain Fecha: 2013-01-01Tipo de documento: ArticuloResumen:We examine the quantum correlations of spin pairs in the cyclic XX spin 1/2 chain in a trans- verse field, through the analysis of the quantum discord, the geometric discord and the information deficit. It is shown that while these quantities provide the same qualitative information, being non- zero for all temperatures and separations and exhibiting the same type of asymptotic behavior for large temperatures or separations, important differences arise in the minimizing local measurement that defines them. Whereas the quantum discord prefers a spin measurement perpendicular to the transverse field, the geometric discord and information deficit exhibit a perpendicular to parallel transition as the field increases, which subsists at all temperatures and for all separations. More- over, it is shown that such transition signals the change from a Bell state to an aligned separable state of the dominant eigenstate of the reduced density matrix of the pair. Full exact results for both the thermodynamic limit and the finite chain are provided, through the Jordan-Wigner fermionization.Compartir:
Generalized conditional entropy in bipartite quantum systems Fecha: 2013-01-01Tipo de documento: ArticuloResumen:We analyze, for a general concave entropic form, the associated conditional entropy of a quantum system A+B, obtained as a result of a local measurement on one of the systems (B). This quantity is a measure of the average mixedness of A after such measurement, and its minimum over all local measurements is shown to be the associated entanglement of formation between A and a purifying third system C. In the case of the von Neumann entropy, this minimum determines also the quantum discord. For classically correlated states and mixtures of a pure state with the maximally mixed state, we show that the minimizing measurement can be determined analytically and is universal, i.e., the same for all concave forms. While these properties no longer hold for general states, we also show that in the special case of the linear entropy, an explicit expression for the associated conditional entropy can be obtained, whose minimum among projective measurements in a general qudit-qubit state can be determined analytically, in terms of the largest eigenvalue of a simple 3 × 3 correlation matrix. Such minimum determines the maximum conditional purity of A, and the associated minimizing measurement is shown to be also universal in the vicinity of maximal mixedness. Results for X states, including typical reduced states of spin pairs in XY chains at weak and strong transverse fields, are also provided and indicate that the measurements minimizing the von Neumann and linear conditional entropies are typically coincident in these states, being determined essentially by the main correlation. They can differ, however, substantially from that minimizing the geometric discord.Compartir:
Measurements, quantum discord, and parity in spin-1 systems Fecha: 2012-08-03Tipo de documento: ArticuloResumen:We consider the evaluation of the quantum discord and other related measures of quantum correlations in a system formed by a spin-1 and a complementary spin system. A characterization of general projective measurements in such system in terms of spin averages is thereby introduced, which allows one to easily visualize their deviation from standard spin measurements. It is shown that the measurement optimizing these measures corresponds in general to a nonspin measurement. The important case of states that commute with the total Sz spin-parity is discussed in detail, and the general stationary measurements for such states (parity preserving measurements) are identified. Numerical and analytical results for the quantum discord, the geometric discord, and the one way information deficit in the relevant case of a mixture of two aligned spin-1 states are also presented.Compartir:
Entanglement and area laws in weakly correlated gaussian states Fecha: 2012-01-01Tipo de documento: ArticuloResumen:We examine the evaluation of entanglement measures in weakly correlated gaussian states. It is shown that they can be expressed in terms of the singular values of a particular block of the generalized contraction matrix. This result enables to obtain in a simple way asymptotic expressions and related area laws for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also pairs of arbitrary subsystems. As illustration, we consider different types of contiguous and noncontiguous blocks in two dimensional lattices. Exact asymptotic expressions are provided for both first neighbor and full range couplings, which lead in the first case to area laws depending on the orientation and separation of the blocks.Compartir:
Entanglement of two harmonic modes coupled by angular momentum Autores:Rebón, Lorena Rossignoli, Raúl Dante Fecha: 2011-11-18Tipo de documento: ArticuloResumen:We examine the entanglement induced by an angular momentum coupling between two harmonic systems. The Hamiltonian corresponds to that of a charged particle in a uniform magnetic field in an anisotropic quadratic potential or, equivalently, to that of a particle in a rotating quadratic potential. We analyze both the vacuum and thermal entanglement, thereby obtaining analytic expressions for the entanglement entropy and negativity through the Gaussian state formalism. It is shown that vacuum entanglement diverges at the edges of the dynamically stable sectors, increasing with the angular momentum and saturating for strong fields, whereas at finite temperature entanglement is nonzero just within a finite field or frequency window and no longer diverges. Moreover, the limit temperature for entanglement is finite in the whole stable domain. The thermal behavior of the Gaussian quantum discord and its difference from the negativity is also discussed.Compartir:
Generalized measures of quantum correlations for mixed states Fecha: 2011-11-17Tipo de documento: ArticuloResumen:The exponential speedup achieved in certain quantum algorithms based on mixed states with negligible entanglement has renewed the interest on alternative measures of quantum correlations. Here we discuss a general measure of quantum correlations for composite systems based on generalized entropic functions, defined as the minimum information loss due to a local measurement. For pure states, the present measure becomes an entanglement entropy, i.e., it reduces to the generalized entropy of the reduced state. However, for mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Quadratic measures of quantum correlations can be derived as particular cases of the present formalism. The minimum information loss due to a joint local measurement is also considered. The evaluation of these measures in a simple yet relevant case is also discussed.Compartir:
Quantum correlations and least disturbing local measurements Fecha: 2011-11-01Tipo de documento: ArticuloResumen:We examine the evaluation of the minimum information loss due to an unread local measurement in mixed states of bipartite systems, for a general entropic form. Such a quantity provides a measure of quantum correlations, reducing for pure states to the generalized entanglement entropy, while in the case of mixed states it vanishes just for classically correlated states with respect to the measured system, as the quantum discord. General stationary conditions are provided, together with their explicit form for general two-qubit states. Closed expressions for the minimum information loss as measured by quadratic and cubic entropies are also derived for general states of two-qubit systems. As an application, we analyze the case of states with maximally mixed marginals, where a general evaluation is provided, as well as X states and the mixture of two aligned states.Compartir:
Evaluation of entanglement measures in spin systems with the random phase approximation Fecha: 2011-07-01Tipo de documento: ArticuloResumen:We discuss a general formalism based on the mean field plus random phase approximation (RPA) for the evaluation of entanglement measures in the ground state of spin systems. The method provides a tractable scheme for determining the entanglement entropy as well as the negativity of finite subsystems, which becomes analytic in the case of systems with translational invariance, in one or D dimensions. The approach improves as the spin increases, and also as the interaction range or connectivity increases. Illustrative results for different types of entanglement entropies (single site, block and comb) in the ground state of a small spin lattice with ferromagnetic type XY couplings in a transverse field are shown and compared with the exact numerical result. Effects arising from symmetry breaking at the mean field level are also discussed.Compartir:
Even-odd entanglement in boson and spin systems Fecha: 2011-04-22Tipo de documento: PreprintResumen:We examine the entanglement entropy of the even half of a translationally invariant finite chain or lattice in its ground state. This entropy measures the entanglement between the even and odd halves (each forming a 'comb' of n/2 sites) and can be expected to be extensive for short-range couplings away from criticality. We first consider bosonic systems with quadratic couplings, where analytic expressions for arbitrary dimensions can be provided. The bosonic treatment is then applied to finite spin chains and arrays by means of the random-phase approximation. Results for first-neighbor anisotropic XY couplings indicate that, while at strong magnetic fields this entropy is strictly extensive, at weak fields important deviations arise, stemming from parity-breaking effects and the presence of a factorizing field (in the vicinity of which it becomes size-independent and identical to the entropy of a contiguous half). Exact numerical results for small spin s chains are shown to be in agreement with the bosonic random-phase approximation prediction.Compartir:
Generalized entropic measures of quantum correlations Fecha: 2010-11-30Tipo de documento: PreprintResumen:We propose a general measure of nonclassical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.Compartir:
Quantum discord in finite XY chains Fecha: 2010-10-19Tipo de documento: ArticuloResumen:We examine the quantum discord between two spins in the exact ground state of finite spin-1/2 arrays with anisotropic XY couplings in a transverse field B. It is shown that in the vicinity of the factorizing field Bs, the discord approaches a common finite non-negligible limit which is independent of the pair separation and the coupling range. An analytic expression of this limit is provided. The discord of a mixture of aligned pairs in two different directions, crucial for the previous results, is analyzed in detail, including the evaluation of coherence effects, relevant in small samples and responsible for a parity splitting at Bs. Exact results for finite chains with first-neighbor and full-range couplings and their interpretation in terms of such mixtures are provided.Compartir:
Evaluation of ground state entanglement in spin systems with the random phase approximation Fecha: 2010-01-01Tipo de documento: PreprintResumen:We discuss a general treatment based on the mean field plus random phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method, becoming straightforward in translationally invariant arrays. The method is examined in arrays of arbitrary spin with XY Z couplings of general range in a uniform transverse field, where the RPA around both the normal and parity breaking mean field state, together with parity restoration effects, are discussed in detail. In the case of a uniformly connected XY Z array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin s pair is also discussed.Compartir:
Separability and entanglement in finite dimer-type chains in general transverse fields Fecha: 2010-01-01Tipo de documento: ArticuloResumen:We determine the conditions under which general dimer-type spin chains with XYZ couplings of arbitrary range in a general transverse field will exhibit an exactly separable parity-breaking eigenstate. We also provide sufficient conditions which ensure that it will be a ground state. We then examine the exact side limits at separability of the entanglement between any two spins in a finite chain, showing that in the vicinity of separability, the system will loose all signatures of dimerization, with pairwise entanglement approaching infinite range and becoming independent of separation and interaction range. The possibility of a nonuniform exactly separable ground state induced by an alternating field is also shown. As illustration, we examine the behavior of the pairwise entanglement in a finite XY dimer chain under a uniform as well as alternating field. Related aspects of the magnetization are also discussed.Compartir:
Stability, complex modes, and nonseparability in rotating quadratic potentials Fecha: 2009-06-08Tipo de documento: ArticuloResumen:We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential in the presence of a uniform magnetic field. It is shown that the unstable system exhibits a rich structure, with complex normal modes as well as nonstandard modes of evolution characterized by equations of motion which cannot be decoupled (nonseparable cases). It is also shown that in some unstable cases the dynamics can be stabilized by increasing the magnetic field or tuning the rotational frequency, giving rise to dynamical stability or instability windows. The evolution in general nondiagonalizable cases is as well discussed.Compartir:
Factorization and entanglement in general XYZ spin arrays in nonuniform transverse fields Fecha: 2009-01-01Tipo de documento: ArticuloResumen:We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through XYZ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the XXZ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the jth spin in an open spin s chain for different values of s and j are as well provided.Compartir:
Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation Fecha: 2008-10-20Tipo de documento: ArticuloResumen:We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for uniform mean fields it requires just the solution of simple local-type RPA equations. As test and application, we use the method for evaluating the entanglement between two spins in cyclic Evaluation of pairwise entanglement in translationally invariant systems with the random phase approximation chains with both long- and short-range anisotropic XY-type couplings in a uniform transverse magnetic field. The approach is shown to provide an accurate analytic description of the concurrence for strong fields, for any coupling range, pair separation, or chain size, where it predicts an entanglement range which can be at most twice that of the interaction. It also correctly predicts the existence of a separability field together with full entanglement range in its vicinity. The general accuracy of the approach improves as the range of the interaction increases.Compartir:
Entanglement of finite cyclic chains at factorizing fields Fecha: 2008-01-01Tipo de documento: ArticuloResumen:We examine the entanglement of cyclic spin-1/2 chains with anisotropic XYZ Heisenberg couplings of arbitrary range at transverse factorizing magnetic fields. At these fields the system exhibits a degenerate symmetry-breaking separable ground state (GS). It is shown, however, that the side limits of the GS pairwise entanglement at these fields are actually nonzero in finite chains, corresponding such fields to a GS spin-parity transition. These limits exhibit universal properties like being independent of the pair separation and interaction range, and are directly related to the magnetization jump. Illustrative exact results are shown for chains with (I) full range and (II) nearest-neighbor couplings. Global entanglement properties at such points are also discussed.Compartir:
Thermal entanglement in fully connected spin systems and its random-phase-approximation description Fecha: 2008-01-01Tipo de documento: ArticuloResumen:We examine the thermal pairwise entanglement in a symmetric system of n spins fully connected through anisotropic XYZ-type couplings embedded in a transverse magnetic field. We consider both the exact evaluation together with that obtained with the static path+random phase approximation RPA and the ensuing mean field+RPA. The latter is shown to provide an accurate analytic description of both the parallel and antiparallel thermal concurrence in large systems. We also analyze the limit temperature for pairwise entanglement, which is shown to increase for large fields and to decrease logarithmically with increasing n. Special finite-size effects are also discussed.Compartir:
Description of thermal entanglement with the static path plus random-phase approximation Fecha: 2007-08-01Tipo de documento: ArticuloResumen:We discuss the application of the static path plus random-phase approximation sSPA+RPAd and the ensuing mean field+RPA treatment to the evaluation of entanglement in composite quantum systems at finite temperature. These methods involve just local diagonalizations and the determination of the generalized collective vibrational frequencies. As an illustration, we evaluate the pairwise entanglement in a fully connected XXZ chain of n spins at finite temperature in a transverse magnetic field b. It is shown that already the mean field+RPA provides an accurate analytic description of the concurrence below the mean field critical region (|b| < bc), exact for large n, whereas the full SPA+RPA is able to improve results for finite systems in the critical region. It is proven as well, that for T > 0 weak entanglement also arises when the ground state is separable (|b| > bc), with the limit temperature for pairwise entanglement exhibiting quite distinct regimes for (|b| < bc) and (|b| > bc).Compartir:
Entanglement between distant qubits in cyclic XX chains Fecha: 2007-03-30Tipo de documento: ArticuloResumen:We evaluate the exact concurrence between any two spins in a cyclic XX chain of n spins placed in a uniform transverse magnetic field, at both zero and finite temperature, by means of the Jordan-Wigner transformation plus a number-parity-projected statistics. It is shown that, while at T = 0 there is always entanglement between any two spins in a narrow field interval before the transition to the aligned state, at low but nonzero temperatures the entanglement remains nonzero for arbitrarily high fields, for any pair separation L, although its magnitude decreases exponentially with increasing field. It is also demonstrated that the associated limit temperatures approach a constant nonzero value in this limit, which decreases as L⁻² for L ⪡ n , but exhibit special finite-size effects for distant qubits (L ≈ n ∕ 2) . Related aspects such as the different behavior of even and odd antiferromagnetic chains, the existence of n ground-state transitions, and the thermodynamic limit n → ∞ are also discussed.Compartir:
Majorization properties of generalized thermal distributions Fecha: 2006-08-01Tipo de documento: ArticuloResumen:We examine the majorization properties of general thermal-like mixed states depending on a set of parameters. Sufficient conditions which ensure the increase in mixedness, and hence of any associated entropic form, when these parameters are varied, are identified. We then discuss those exhibiting a power law distribution, showing that they can be characterized by two distinct mixing parameters, one associated with temperature and the other with the non-extensivity index q. Illustrative numerical results are also provided.Compartir:
Global entanglement in XXZ chains Fecha: 2006-02-01Tipo de documento: ArticuloResumen:We examine the thermal entanglement of XXZ-type Heisenberg chains in the presence of a uniform magnetic field along the z axes through the evaluation of the negativity associated with bipartitions of the whole system and subsystems. Limit temperatures for nonzero global negativities are shown to depend on the asymmetry Δ, but not on the uniform field, and can be much higher than those limiting pairwise entanglement. It is also shown that global bipartite entanglement may exist for T > 0 even for Δ ≥ 1, i.e., when the system is fully aligned (and hence separable) at T = 0, and that the bipartition leading to the highest limit temperature depends on Δ.Compartir:
Complex modes in unstable quadratic bosonic forms Fecha: 2005-09-02Tipo de documento: ArticuloResumen:We discuss the necessity of using nonstandard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to non-Hermitian coordinates and momenta and are associated with complex frequencies. As application, we examine a bosonic version of a BCS-like pairing Hamiltonian, which, in contrast with the fermionic case, is stable just for limited values of the gap parameter and requires the use of the present extended treatment for a general diagonal representation. The dynamical stability of such forms and the occurrence of nondiagonalizable cases are also discussed.Compartir:
Global thermal entanglement in n-qubit systems Fecha: 2005-07-01Tipo de documento: ArticuloResumen:We examine the entanglement of thermal states of n spins interacting through different types of XY couplings in the presence of a uniform magnetic field, by evaluating the negativities of all possible bipartite partitions of the whole system and of subsystems. We consider both the case where every qubit interacts with all others and where just nearest neighbors interact in a one-dimensional chain. Limit temperatures for nonzero negativities are also evaluated and compared with the mean field critical temperature. It is shown that limit temperatures of global negativities are strictly independent of the magnetic field in all XXZ models, in spite of the quantum transitions that these models may exhibit at zero temperature, while in anisotropic models they always increase for sufficiently large fields. Results also show that these temperatures are higher than those limiting pairwise entanglement.Compartir:
Separability conditions and limit temperatures for entanglement detection in two-qubit Heisenberg XYZ models Fecha: 2004-05-11Tipo de documento: ArticuloResumen:We examine the entanglement of general mixed states of a two-qubit Heisenberg XYZ chain in the presence of a magnetic field, and its detection by means of different criteria. Both the exact separability conditions and the weaker conditions implied by the disorder and the von Neumann entropic criteria are analyzed. The ensuing limit temperatures for entanglement in thermal states of different XYZ models are then examined and compared with the limit temperature of the symmetry-breaking solution in a mean-field-type approximation. The latter, though generally lower, can also be higher than the exact limit temperature for entanglement in certain cases, indicating that symmetry breaking does not necessarily entail entanglement. The reentry of entanglement for increasing temperatures is also discussed.Compartir:
Violation of majorization relations in entangled states and its detection by means of generalized entropic forms Fecha: 2003-04-01Tipo de documento: ArticuloResumen:We examine the violation of the majorization relations between the eigenvalues of the full and reduced density operators of entangled states of composite systems and its detection using generalized entropic forms based on arbitrary concave functions. It is shown that the violation of these relations may not always be detected by the conditional von Neumann and Tsallis entropies (for any q > 0). Families of smooth entropic forms which are always able to detect such violations are, however, provided. These features are then examined for particular sets of mixed states in a two-qudit system, which for d ≥ 3 may exhibit different types of violation of the majorization relations. Comparison with the Peres criterion for separability is also shown.Compartir:
Generalized entropic criterion for separability Fecha: 2002-10-11Tipo de documento: ArticuloResumen:We discuss the entropic criterion for separability of compound quantum systems for general nonadditive entropic forms based on arbitrary concave functions f. For any separable state, the generalized entropy of the whole system is shown to be not smaller than that of the subsystems, for any choice of f, providing thus a necessary criterion for separability. Nevertheless, the criterion is not sufficient and examples of entangled states with the same property are provided. This entails, in particular, that the conjecture about the positivity of the conditional Tsallis entropy for all q, a more stringent requirement than the positivity of the conditional von Neumann entropy, is actually a necessary but not sufficient condition for separability in general. The direct relation between the entropic criterion and the largest eigenvalues of the full and reduced density operators of the system is also discussed.Compartir:
Generalized nonadditive entropies and quantum entanglement Fecha: 2002-04-10Tipo de documento: ArticuloResumen:We examine the inference of quantum density operators from incomplete information by means of the maximization of general nonadditive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1/2 system, the formalism allows one to avoid fake entanglement for data based on the Bell-Clauser-Horne-Shimony-Holt observable, and, in general, on any set of Bell constraints. Particular results obtained with the Tsallis entropy and with an introduced exponential entropic form are also discussed.Compartir:
Microscopic treatment of fluctuations in finite quantum systems Fecha: 1996-06-01Tipo de documento: ArticuloResumen:We describe a fully microscopic treatment of fluctuations in correlated finite systems at finite temperature, based on the static path approximation (SPA) to the partition function, which incorporates the large amplitude statistical fluctuations around mean field, and the ensuing SPA+RPA approach, which includes in addition the small amplitude quantal fluctuations. An application to the description of pairing, shape and orientation fluctuations in hot nuclei is then given. The treatment of constraints is also discussed.Compartir:
Maximum Entropy Variational Approach to Collective States Fecha: 1993-01-01Tipo de documento: Capitulo de libroResumen:An approximation to the energy eigenstates of a many-body system, based on a previously introduced maximum entropy approach to the ground state, is developed and applied to a monopole fermion system. An excellent agreement with the exact eigenstates is obtained over the whole range of the pertinent coupling constant.Compartir:
Finite Temperature Correlated Mean Field Treatments and Information Theory Fecha: 1992-01-01Tipo de documento: Capitulo de libroResumen:A general self-consistent scheme for approximating statistical operators is discussed within the context of Information Theory. As an application, a special correlated finite temperature mean field approximation is derived and applied to many-fermion systems. A substantial improvement over conventional approaches such as finite temperature Hartree-Fock and finite temperature BCS is obtained in finite systems.Compartir:
Tratamientos canónicos de campo medio a temperatura finita Autores:Rossignoli, Raúl Dante Fecha: 1991-01-01Tipo de documento: ArticuloResumen:Se propone un método para realizar tratamientos canónicos de campo medio y de orden superior a temperatura finita. Se obtienen definidas mejoras sobre el tratamiento usual (gran canónico) de Hartrce - Fock térmico.Compartir:
High-temperature superfluidity with abnormal fermionic occupancy Fecha: 1991-01-01Tipo de documento: ArticuloResumen:We examine a Lipkin based two-level pairing model at finite temperature and in the thermodynamic limit. Whereas at T=0 the model exhibits a superconducting ground state for sufficiently high values of the coupling constant, a partially superconducting phase in whichsome of the particles are paired, is found to survive at high temperatures in a special treatment. This phase is a mixture of “abnormally-occupied” eigenstates, which lie at higher energy, of the interactionless model Hamiltonian.Compartir:
Transiciones de fase y entropía cuántica Autores:Arrachea, Liliana Canosa, Norma Beatriz Plastino, Ángel Luis Portesi, Mariela Adelina Rossignoli, Raúl Dante Fecha: 1991-01-01Tipo de documento: ArticuloResumen:Se examina la posibilidad de predecir las transiciones de fase del estado fundamental de un sistema cuántico finito, conociendo la entropía cuántica de estos estados, definida en base a la Teoría de la Información.Compartir:
Inferencia de espectros de energía y teoría de la información Fecha: 1991-01-01Tipo de documento: ArticuloResumen:Se analiza la posibilidad de inferir los aspectos de energía y los autoestados correspondientes, en base a información incompleta referida al estado fundamental del sistema. Se examina asimismo, la posibilidad de considerar como dato el valor medio de un hamiltoniano parcialmente conocido.Compartir:
Temporal Evolution of Fluctuations Fecha: 1990-01-01Tipo de documento: Objeto de conferenciaResumen:The Time Dependent Hartree-Fock (TDHF) approximation1,2 constitutes the basic tool for dealing with the evolution of an uncorrelated many-body wave function.Compartir:
Principio de máxima entropía en sistemas cuánticos de muchos cuerpos Fecha: 1990-01-01Tipo de documento: ArticuloResumen:Se presenta un método sistemático para la inferenia del estado fundamental de un sistema de muchos cuerpos en base a información incompleta. El esquema, basado en el principio de máxima entropía, es también apto para la construcción de aproximaciones variacionales. Los resultados indican que excelentes predicciones, superiores a aquellas brindadas por tratamientos proyectados de campo medio, pueden ser obtenidas a partir de un conjunto reducido de valores medios o parámetros variacionales, inclusive en regiones críticas.Compartir:
Aproximación general autoconsistente para operadores estadísticos Fecha: 1989-01-01Tipo de documento: ArticuloResumen:Se introduce una aproximación general autoconsistente para operadores estadísticos. El esquema se reduce a una descripción estadística generalizada de campo medio al ser aplicado a operadores de un cuerpo. No obstante, el presente contexto permite visualizar la aproximación desde un punto de vista distinto, y posibilita además la construcción directa de aproximaciones autoconsistentes de orden superior.Compartir:
Aspectos estadísticos de tratamientos autoconsistentes en sistemas cuánticos de muchos cuerpos Autores:Rossignoli, Raúl Fecha: 1987-01-01Tipo de documento: Tesis de doctoradoResumen:Las aproximaciones autoconsistentes de campo medio constituyen una de las más importantes herramientas teóricas para tratar el problema cuántico de muchos cuerpos, proporcionando una descripción y un punto de partida apropiados para desarrollos más complejos. Dentro de este contexto, el objetivo de esta tesis es extender y analizar las teorías cuánticas de campo medio, tanto estáticas como dinámicas, en base a consideraciones de carácter estadístico, situándolas de este modo dentro de un marco más amplio y flexible que el usual. La idea central que nos anima es la de basar la descripción de un sistema en un conjunto particular de observables, considerados relevantes para el fenómeno en estudio. Este modo de descripción es impulsado por la complejidad del problema cuántico de muchos cuerpos, y además, en ciertos casos por la necesidad de preservar solo la información significativa acerca del sistema. De este modo, se enfoca la atención sobre un subconjunto de variables, descartando las muchas otras restantes por medio de un adecuado esquema aproximado. Las teorías usuales de campo medio constituyen aquel caso especial de nuestro tratamiento en el que el conjunto de observables relevantes se encuentra formado por operadores de un cuerpo. A tales efectos, se desarrolla un formalismo general apropiado que permite abordar este tipo de extensión. Se examinan en profundidad diversos tipos de situaciones específicas, abarcando situaciones de equilibrio (Cap. I-IV), como así también problemas dependientes del tiempo (Cap. V-VI).Compartir:
The minimum norm method for the determination of the charge density from elastic electron scattering data Autores:Miller, H.G. Tzeng, Yiharn Yen, G. D. Canosa, Norma Beatriz Rossignoli, Raúl Dante Plastino, Ángel Luis Fecha: 1986-01-01Tipo de documento: ArticuloResumen:Unphysical behavior in the QR algorithm based least squares determination of the expansion coefficients of the charge density obtained from limited information about the charge form factor occurs when the spread of the singular values in the matrix relating these quantities becomes too large. Setting the smallest singular values equal to zero in the singular value decomposition used in the minimum norm method yields a much more reasonable determination of the charge density. Increasing the size of the basis without increasing the range of the prior information about the charge form factor leads to ambiguities in the determination of the charge density. Numerical results in an analytic model are presented.Compartir:
