scholarly journals Quantum Entanglement and Quantum Discord of Two-Mode Gaussian States in a Thermal Environment

2011 ◽  
Vol 18 (02) ◽  
pp. 175-190 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Sudden Death ◽  
Time Evolution ◽  
Quantum Entanglement ◽  
Quantum Discord ◽  
Thermal Environment ◽  
Quantum Correlations ◽  
Entangled State ◽  
Gaussian State ◽  
Thermal Bath ◽  
Bipartite State

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initially separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and we show that in the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze time evolution of Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and we show that quantum discord decays asymptotically in time under the effect of thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of quantum system.

Quantum discord and entanglement of two atoms in a micromaser-type system

2016 ◽  
Vol 30 (15) ◽  
pp. 1650190
Author(s):  
Xue-Qun Yan ◽  
Fu-Zhong Wang
Keyword(s):  
Time Evolution ◽  
Mixed State ◽  
Quantum Discord ◽  
Type System ◽  
Complete Loss ◽  
Entangled State ◽  
Fock State

The correlations dynamics of two atoms in the case of a micromaser-type system is investigated. We show that the entangled state can be created by initially maximally mixed state and there exist collapse and revival phenomena for the time evolutions of both entanglement and quantum discord under the system considered as the field is initially in the Fock state. Our results confirm that entanglement and quantum discord have similar behaviors in certain time ranges, such as their oscillations during the time evolution being almost in phase, but they also present significant differences, such as quantum discord being maintained even after the complete loss of entanglement. Furthermore, we exhibit clearly that the dynamics of quantum discord under the action of environment are intimately related to the generation and evolution of entanglement.

Quantum correlations and coherence dynamics in qutrit–qutrit systems under mixed classical environmental noises

2017 ◽  
Vol 15 (06) ◽  
pp. 1750047 ◽  
Author(s):  
Tsamouo Tsokeng Arthur ◽  
Tchoffo Martin ◽  
Lukong Cornelius Fai
Keyword(s):  
Sudden Death ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Collective Effects ◽  
Markovian Environment ◽  
Dynamic Noise ◽  
Long Time ◽  
Noise Models ◽  
Markovian Regime ◽  
Static Noise

We investigate the dynamics of entanglement, quantum discord (QD) and state coherence in a bipartite and noninteracting spin-qutrits system under mixed classical noises. Specifically, the collective effects of static noise (SN) and random telegraphic noise (RTN) each being coupled with a marginal system, are analyzed. While the static noise models a non-Markovian environment, the dynamic noise can model both a Markovian or a non-Markovian environment, and both dynamics are studied. We show that quantum correlations and coherence may survive the noise degrading effects at sufficiently long time when the Markovian regime of the RTN is considered. Meanwhile, the opposite is found in the non-Markovian regime, wherein the nonmonotonic dynamics of quantum features avoid sudden death phenomena. However, the static noise is more fatal to the survival of quantum correlations and quantum state coherence as compared to the RTN.

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.

QUANTUM CORRELATIONS IN THE ENTANGLEMENT DISTILLATION PROTOCOLS

2013 ◽  
Vol 11 (03) ◽  
pp. 1350029
Author(s):  
SHAO-XIONG WU ◽  
JUN ZHANG ◽  
CHANG-SHUI YU ◽  
HE-SHAN SONG
Keyword(s):  
Quantum Entanglement ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Entangled States ◽  
Entanglement Distillation

We study the quantum correlations between source and target pairs in different protocols of entanglement distillation of one kind of entangled states. We find that there does not exist any quantum correlation in the standard recurrence distillation protocol, while quantum discord and even quantum entanglement are always present in the other two cases of the improved distillation protocols. In the three cases, the distillation efficiency improved with the quantum correlations enhanced.

scholarly journals Local available quantum correlations for Bell Diagonal states and Markovian decoherence

2018 ◽  
Vol 64 (6) ◽  
pp. 662
Author(s):  
Hermann L Albrecht Q ◽  
Douglas F. Mundarain ◽  
Mario I. Caicedo S.
Keyword(s):  
Sudden Death ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Entanglement Sudden Death ◽  
Dissipative Dynamics ◽  
Phase Damping ◽  
Werner States ◽  
Kraus Operators

Local available quantum correlations (LAQCs), as dened by Mundarain et al. [19], are analytically determined for Bell Diagonal states. Using the Kraus operators formalism [10], we analyze the dissipative dynamics of 2-qubit LAQCs under Markovian decoherence. This is done for Werner states under the depolarizing [20] and phase damping channels [21]. Since Werner states are among those that exhibit the so called entanglement sudden death [27], the results are compared with the ones obtained for Quantum Discord [22], as analyzed by Werlang et al. [24], as well as for entanglement, i.e. Concurrence[7]. The LAQCs quantier, as Quantum Discord does, only vanishes asymptotically.

MONOGAMY PROPERTIES OF QUANTUM DISCORD FOR A THREE-QUBIT ENTANGLED STATE

2013 ◽  
Vol 27 (07) ◽  
pp. 1350049 ◽  
Author(s):  
XUE-KE SONG ◽  
TAO WU ◽  
LIU YE
Keyword(s):  
Relative Entropy ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
The Other ◽  
Numerical Calculations ◽  
Entangled State ◽  
Geometric Quantum Discord ◽  
The Given

In this paper, we obtain the pairwise quantum discord for a three-qubit W-class state, and investigate the monogamy property of quantum discord by two different ways (relative entropy-based distance and geometric square-norm distance). Through numerical calculations, we find that a party cannot have maximal quantum correlations with the other two parties simultaneously. For the given state, the quantum correlation between particles 1 and 3 induces limitation on the quantum correlation between them and particle 2. Moreover, the result also shows that the geometric quantum discord of the given W-class state obeys the monogamy property while the entropy quantum discord violates.

Comparative study of quantum discord and geometric discord for generic bipartite states

2014 ◽  
Vol 12 (05) ◽  
pp. 1450027 ◽  
Author(s):  
Bao Liu ◽  
Zheng Hu ◽  
Xi-Wen Hou
Keyword(s):  
Quantum Entanglement ◽  
Quantum Discord ◽  
Mixed States ◽  
High Dimensions ◽  
Euler Parameters ◽  
Bipartite State ◽  
Daunting Task ◽  
Orthogonal Projectors ◽  
Optimal Measurements

The characterization of quantum discord (QD) and geometric discord (GD) has mostly concentrated on two-qubit states since the minimization in both discords is a daunting task for high-dimensional states. Numerical calculations of both discords are carried out for a generic bipartite state. When one-dimensional orthogonal projectors for a local measurement on n-dimensional Hilbert space are realized by the generators and the Euler angles of SU (n), the optimal measurements have a figure of merit that includes n(n - 1) Euler parameters. As an representative example, such projectors and two kinds of algorithms are used to estimate both discords for two-qutrit mixed states in recent literature. The generalized negativity as a measure of quantum entanglement is calculated for reference purposes. For those states with one parameter the discords and the negativity respectively display the nonlinear and the linear function of the parameter, with different turning points. However, they are positively correlated in the suitable ranges of the parameter for those states. The hierarchy of those quantities is discussed as well. Those shed new light on the understanding of QDs and quantum entanglement of mixed states in high-dimensions.

scholarly journals Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 785 ◽  
Author(s):  
Iulia Ghiu ◽  
Roberto Grimaudo ◽  
Tatiana Mihaescu ◽  
Aurelian Isar ◽  
Antonino Messina
Keyword(s):  
Time Evolution ◽  
Quantum Correlation ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Initial State ◽  
Analytical Treatment ◽  
Werner State ◽  
Driven System ◽  
Physical Reasons

We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state.

Quantum Discord of Two Bosonic Modes in Two-Reservoir Model

2013 ◽  
Vol 20 (03) ◽  
pp. 1340003 ◽  
Author(s):  
Aurelian Isar
Keyword(s):  
Quantum Discord ◽  
Open Systems ◽  
Vacuum State ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Reservoir Model ◽  
Bipartite State ◽  
Thermal Environments ◽  
Gaussian Input ◽  
Gaussian Quantum Discord

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable quantum discord for a system consisting of two non-interacting bosonic modes embedded in two independent thermal environments. We describe the evolution of discord in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed vacuum state, we analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal reservoirs. For an initial separable pure state, the Gaussian quantum discord is zero and it keeps this value during the whole evolution of the system.

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