Dynamic of the Gaussian quantum discord and effect of non-Markovian degree

2015 ◽  
Vol 93 (4) ◽  
pp. 481-485
Author(s):  
Xin Liu ◽  
Wei Wu ◽  
Changkui Hu
Keyword(s):  
Markov Process ◽  
Experimental Method ◽  
Dynamic Characteristic ◽  
Quantum Discord ◽  
Thermal State ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Zero Temperature ◽  
The Relationship ◽  
Gaussian Quantum Discord

We study the dynamic of the Gaussian quantum discord in a continuous-variable system subject to a common non-Markovian environment with zero-temperature. By considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that Gaussian discord has a very different dynamic characteristic in a non-Markovian evolution versus a Markov process, and can be created by the memory effect, which features non-Markovianity. We also study the relationship between Gaussian discord and the non-Markovian degree of the environment. The results may offer us an effective experimental method to get more quantum correlations.

scholarly journals THE BALANCE OF QUANTUM CORRELATIONS FOR A CLASS OF FEASIBLE TRIPARTITE CONTINUOUS VARIABLE STATES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345024 ◽  
Author(s):  
STEFANO OLIVARES ◽  
MATTEO G. A. PARIS
Keyword(s):  
Conservation Laws ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Noisy Environment ◽  
Mixed States ◽  
Von Neumann ◽  
Entanglement Of Formation ◽  
Pure States ◽  
Gaussian Quantum Discord

We address the balance of quantum correlations for continuous variable (CV) states. In particular, we consider a class of feasible tripartite CV pure states and explicitly prove two Koashi–Winter-like conservation laws involving Gaussian entanglement of formation (EoF), Gaussian quantum discord and sub-system Von Neumann entropies. We also address the class of tripartite CV mixed states resulting from the propagation in a noisy environment, and discuss how the previous equalities evolve into inequalities.

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.

scholarly journals Quantum Correlation Based on Uhlmann Fidelity for Gaussian States

Entropy ◽  
2018 ◽  
Vol 21 (1) ◽  
pp. 6
Author(s):  
Liang Liu ◽  
Jinchuan Hou ◽  
Xiaofei Qi
Keyword(s):  
Quantum Channel ◽  
Quantum Correlation ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Continuous Variable ◽  
Gaussian States ◽  
Gaussian Quantum Discord ◽  
Geometric Measurement ◽  
Thermal States

A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states.

scholarly journals INTERPLAY BETWEEN QUANTUM PHASE TRANSITIONS AND THE BEHAVIOR OF QUANTUM CORRELATIONS AT FINITE TEMPERATURES

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345032 ◽  
Author(s):  
T. WERLANG ◽  
G. A. P. RIBEIRO ◽  
GUSTAVO RIGOLIN
Keyword(s):  
Phase Transitions ◽  
Critical Point ◽  
Thermodynamic Limit ◽  
Quantum Discord ◽  
Quantum Phase Transitions ◽  
Quantum Correlations ◽  
Infinite Chain ◽  
Quantum Phase ◽  
Absolute Zero ◽  
Zero Temperature

We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions (QPT) that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a QPT.

Thermal geometric discords in a two-qutrit system

2016 ◽  
Vol 14 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Ya-Li Yuan ◽  
Xi-Wen Hou
Keyword(s):  
Magnetic Field ◽  
Quantum Information ◽  
Magnetic Fields ◽  
Weak Magnetic Field ◽  
Quantum Discord ◽  
Quantum Information Processing ◽  
Thermal State ◽  
Quantum Correlations ◽  
High Dimensional ◽  
Lower Temperature

The investigation of quantum discord has mostly focused on two-qubit systems due to the complicated minimization involved in quantum discord for high-dimensional states. In this work, three geometric discords are studied for the thermal state in a two-qutrit system with various couplings, external magnetic fields, and temperatures as well, where the entanglement measured in terms of the generalized negativity is calculated for reference. It is shown that three geometric discords are more robust against temperature and magnetic field than the entanglement negativity. However, all four quantities exhibit a similar behavior at lower temperature and weak magnetic field. Remarkably, three geometric discords at finite temperature reveal the phenomenon of double sudden changes at different magnetic fields while the negativity does not. Moreover, the hierarchy among three discords is discussed. Those adjustable discords with the varied coupling, temperature, and magnetic field are useful for the understanding of quantum correlations in high-dimensional states and quantum information processing.

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.

Dynamics of classical-quantum correlations between two movable mirrors in optomechanics

2020 ◽  
Vol 34 (08) ◽  
pp. 2050066 ◽  
Author(s):  
M. Amazioug ◽  
L. Jebli ◽  
M. Nassik ◽  
N. Habiballah
Keyword(s):  
Thermal State ◽  
Quantum Correlations ◽  
Strong Coupling Regime ◽  
Squeezed Light ◽  
Fabry Perot ◽  
Classical Quantum ◽  
Rotating Wave ◽  
Quantum Mutual Information ◽  
Down Conversion ◽  
Gaussian Quantum Discord

We study the dynamics of classical-quantum correlations in the nonadiabatic regime, using the rotating wave approximation (RWA), between two movable mirrors of two spatially separated Fabry–Pérot cavities, each of the two cavities having a movable end-mirror and coupled to a two-mode squeezed light from spontaneous parametric down-conversion. This work completes our previous work [M. Amazioug, M. Nassik and N. Habiballah, Eur. Phys. J. D 72, 171 (2018)] where we have studied the transfer of quantum correlations in steady state. The Bures distance is used to quantify the amount of entanglement of the symmetrical squeezed thermal state, and the Gaussian quantum discord is considered to quantify the quantumness of the quantum correlations even though the two movable mirrors are separable. Furthermore, total correlations are quantified using quantum mutual information. Indeed, these three indicators depend mainly on the temperature of the movable mirror and the squeezing parameter in strong coupling regime.

scholarly journals A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1190
Author(s):  
Liang Liu ◽  
Jinchuan Hou ◽  
Xiaofei Qi
Keyword(s):  
Quantum Correlation ◽  
Quantum Discord ◽  
Continuous Variable ◽  
Gaussian State ◽  
Product State ◽  
Gaussian States ◽  
System A ◽  
Gaussian Channels ◽  
The Mean ◽  
Gaussian Quantum Discord

Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

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