Studying quantum correlations dynamics in the phase space for continuous-variable Werner states and Bell-diagonal states

2019 ◽  
Vol 16 (07) ◽  
pp. 1950109
Author(s):  
Fatima-Zahra Siyouri ◽  
Hicham Ait Mansour ◽  
Fadoua Elbarrichi
Keyword(s):  
Wigner Function ◽  
Quantum Discord ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Quantum Systems ◽  
Qubit System ◽  
Classical Correlations ◽  
Werner States ◽  
System F

We investigate the ability of Wigner function to reveal and measure general quantum correlations in two-qubit open system. For this purpose, we analyze comparatively their dynamics for two different states, continuous-variable Werner states (CWS) and Bell-diagonal states (BDS), independently interacting with dephasing reservoirs. Then, we explore the effects of decreasing the degree of non-Markovianity on their behavior. We show that the presence of both quantum entanglement and quantum discord allow to have a negative Wigner function, in contrast to the result obtained for the closed two-qubit system [F. Siyouri, M. El Baz and Y. Hassouni, The negativity of Wigner function as a measure of quantum correlations, Quantum Inf. Process. 15(10) (2016) 4237–4252]. In fact, we conclude that negativity of Wigner function can be used to capture and quantify the amount of general non-classical correlations in open quantum systems.

scholarly journals DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345053 ◽  
Author(s):  
ROSARIO LO FRANCO ◽  
BRUNO BELLOMO ◽  
SABRINA MANISCALCO ◽  
GIUSEPPE COMPAGNO
Keyword(s):  
Quantum Discord ◽  
Open Quantum Systems ◽  
Dynamical Behavior ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Primary Interest ◽  
Common Environment ◽  
Classical Counterpart ◽  
Qubit System ◽  
Dynamics Of Correlations

Knowledge of the dynamical behavior of correlations with no classical counterpart, like entanglement, nonlocal correlations and quantum discord, in open quantum systems is of primary interest because of the possibility to exploit these correlations for quantum information tasks. Here we review some of the most recent results on the dynamics of correlations in bipartite systems embedded in non-Markovian environments that, with their memory effects, influence in a relevant way the system dynamics and appear to be more fundamental than the Markovian ones for practical purposes. Firstly, we review the phenomenon of entanglement revivals in a two-qubit system for both independent environments and a common environment. We then consider the dynamics of quantum discord in non-Markovian dephasing channel and briefly discuss the occurrence of revivals of quantum correlations in classical environments.

scholarly journals Universal non-Markovianity detection in hybrid open quantum systems

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Jiří Svozilík ◽  
Raúl Hidalgo-Sacoto ◽  
Ievgen I. Arkhipov
Keyword(s):  
Quantum System ◽  
Wigner Function ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Continuous Variables ◽  
Open Quantum ◽  
Hybrid Quantum Systems

Abstract A universal characterization of non-Markovianity for any open hybrid quantum systems is presented. This formulation is based on the negativity volume of the generalized Wigner function, which serves as an indicator of the quantum correlations in any composite quantum systems. It is shown, that the proposed measure can be utilized for any single or multi-partite quantum system, containing any discrete or continuous variables. To demonstrate its power in revealing non-Markovianity in such quantum systems, we additionally consider a few illustrative examples.

NON-MARKOVIAN OPEN QUANTUM SYSTEMS: SYSTEM–ENVIRONMENT CORRELATIONS IN DYNAMICAL MAPS

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1617-1634 ◽  
Author(s):  
CÉSAR A. RODRÍGUEZ-ROSARIO ◽  
E. C. G. SUDARSHAN
Keyword(s):  
Master Equation ◽  
Quantum Discord ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Complete Positivity ◽  
System Environment ◽  
Open Quantum ◽  
Mathematical Properties ◽  
Classical Correlations ◽  
The Relationship

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

scholarly journals A study of quantum correlations in open quantum systems

2011 ◽  
Vol 11 (7&8) ◽  
pp. 541-562
Author(s):  
Indranil Chakrabarty ◽  
Subhashish Banerjee ◽  
Nana Siddharth
Keyword(s):  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Bell’S Inequality ◽  
Mixed States ◽  
Classical Correlation ◽  
Bell's Inequality ◽  
Qubit System ◽  
Dynamical Parameters ◽  
Potential Resource

In this work, we study quantum correlations in mixed states. The states studied are modeled by a two-qubit system interacting with its environment via a quantum non demolition (purely dephasing) as well as dissipative type of interaction. The entanglement dynamics of this two qubit system is analyzed. We make a comparative study of various measures of quantum correlations, like Concurrence, Bell's inequality, Discord and Teleportation fidelity, on these states, generated by the above evolutions. We classify these evoluted states on basis of various dynamical parameters like bath squeezing parameter $r$, inter-qubit spacing $r_{12}$, temperature $T$ and time of system-bath evolution $t$. In this study, in addition we report the existence of entangled states which do not violate Bell's inequality, but can still be useful as a potential resource for teleportation. Moreover we study the dynamics of quantum as well as classical correlation in presence of dissipative coherence.

Thermal quantum correlations in the two-qubit Heisenberg XYZ spin chain with Dzyaloshinskii–Moriya interaction

2021 ◽  
pp. 2150074
Author(s):  
Youssef Khedif ◽  
Mohammed Daoud
Keyword(s):  
Quantum Correlations ◽  
Thermal Fluctuations ◽  
Quantum Nonlocality ◽  
Chain Model ◽  
Trace Distance ◽  
Heisenberg Spin ◽  
Logarithmic Negativity ◽  
Qubit System ◽  
Classical Correlations ◽  
Moriya Interaction

We investigate the quantum correlations of a two-qubit XYZ Heisenberg spin-1/2 chain model with Dzyaloshinskii–Moriya interaction. The two-qubit system is considered in thermal equilibrium. The variations of logarithmic negativity, uncertainty-induced quantum nonlocality (UIN) and trace distance discord, versus the parameters characterizing the system, are analyzed. The results show that the UIN measure captures quantum correlations that cannot be revealed by entanglement and trace discord. We also show that the Dzyaloshinskii–Moriya interaction enhances the non-classical correlations between the spins and can weaken the undesirable destructive effects of thermal fluctuations. In addition, an entangled–unentangled phase transition can be detected from the behavior of logarithmic negativity.

Dynamics of Interacting Classical and Quantum Systems

2011 ◽  
Vol 18 (04) ◽  
pp. 339-351 ◽  
Author(s):  
Dariusz Chruściński ◽  
Andrzej Kossakowski ◽  
Giuseppe Marmo ◽  
E. C. G. Sudarshan
Keyword(s):  
Characteristic Feature ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Main Idea ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Quantum States ◽  
Algebra Of Observables ◽  
Classical Quantum ◽  
True Quantum

We analyze the dynamics of coupled classical and quantum systems. The main idea is to treat both systems as true quantum ones and impose a family of superselection rules which imply that the corresponding algebra of observables of one subsystem is commutative and hence may be treated as a classical one. Equivalently, one may impose a special symmetry which restricts the algebra of observables to the 'classical' subalgebra. The characteristic feature of classical-quantum dynamics is that it leaves invariant a subspace of classical-quantum states, that is, it does not create quantum correlations as measured by the quantum discord.

QUANTUM DISCORD UNDER SYSTEM–ENVIRONMENT COUPLING: THE TWO-QUBIT CASE

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345054 ◽  
Author(s):  
JIN-SHI XU ◽  
CHUAN-FENG LI
Keyword(s):  
Quantum Discord ◽  
Open Quantum Systems ◽  
Short Review ◽  
Quantum Systems ◽  
External Control ◽  
Control Effect ◽  
Fundamental Physics ◽  
System Environment ◽  
Open Quantum ◽  
Distinct Property

Open quantum systems have attracted great attention, since inevitable coupling between quantum systems and their environment greatly affects the features of interest of these systems. Quantum discord, is a measure of the total nonclassical correlation in a quantum system that includes, but is not exclusive to, the distinct property of quantum entanglement. Quantum discord can exist in separated quantum states and plays an important role in many fundamental physics problems and practical quantum information tasks. There have been numerous investigations on quantum discord and its counterpart classical correlation. This short review focuses on highlighting the system–environment dynamics of two-qubit quantum discord and the influence of initial system–environment correlations on the dynamics of open quantum systems. The external control effect on the dynamics of open quantum systems are involved. Several related experimental works are discussed.

scholarly journals GAUSSIAN GEOMETRIC DISCORD

2011 ◽  
Vol 09 (07n08) ◽  
pp. 1773-1786 ◽  
Author(s):  
GERARDO ADESSO ◽  
DAVIDE GIROLAMI
Keyword(s):  
Quantum Discord ◽  
Gaussian Quadrature ◽  
Continuous Variable ◽  
Upper And Lower Bounds ◽  
Gaussian States ◽  
Physical Constraints ◽  
Geometric Measure ◽  
Classical Correlations ◽  
Qubit States ◽  
Thermal States

We extend the geometric measure of quantum discord, introduced and computed for two-qubit states, to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.

scholarly journals Generation of Quantum Correlations in Bipartite Gaussian Open Quantum Systems

2018 ◽  
Vol 173 ◽  
pp. 01006 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Open Systems ◽  
Thermal Environment ◽  
Open Quantum Systems ◽  
Quantum Correlations ◽  
Quantum Systems ◽  
Thermal Bath ◽  
Initial State ◽  
Entanglement Generation ◽  
Strength Of Interaction ◽  
Zero Values

We describe the generation of quantum correlations (entanglement, discord and steering) in a system composed of two coupled non-resonant bosonic modes immersed in a common thermal reservoir, in the framework of the theory of open systems. We show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and strength of interaction between the two bosonic modes. We also show that for initial uni-modal squeezed states Gaussian discord can be generated for all non-zero values of the strength of interaction between the modes. Likewise, for an initial separable state, a generation of Gaussian steering may take place temporarily, for definite values of the parameters characterizing the initial state and the thermal environment, and the strength of coupling between the two modes.

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