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Chinese Physics B

Dynamics of measurement-induced non-locality and geometric discord with initial system—environment correlations

Rui-Lin Xiao, Xing Mao Xiao, Wo-Jun Zhong

Published Aug 1, 2013• 5 citations
Publisher

Abstract

We analyze the dynamics of geometric measure of discord (GMOD) and measurement-induced non-locality (MIN) in the presence of initial system—reservoir correlations without Born and Markov approximation. Although the initial system—environment states have the same reduced density matrices for both the system and environment, the effects of different initial system—environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.

DOI
10.1088/1674-1056/22/8/080306

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Abstract We investigate the time evolution of quantum correlations of a hybrid qubit-qutrit system under the classical Ornstein-Uhlenbeck (OU) noise. Here we consider two different one-parameter families of qubit-qutrit states which independently interact with the non-Markovian reservoirs. A comparison with the Markovian dynamics reveals that for the same set of initial condition parameters, the non-Markovian behavior of the environment plays an important role in the enhancement of the survival time of quantum correlations. In addition, it is observed that the non-Markovian strength ( γ / Γ ) has a positive impact on the correlations time. For the initial separable states it is found that there is a finite time interval in which the geometric quantum discord is frozen despite the presence of a noisy environment and that interval can be further prolonged by using the non-Markovian property. Moreover, its decay can be significantly delayed .
We investigate the time evolution of quantum correlations, which are measured by Gaussian quantum discord in a continuous-variable bipartite system subject to common and independent non-Markovian environments. Considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that quantum correlations can be created during the non-Markovian evolution, which is different from the Markovian process. Furthermore, we find that the temperature is a key factor during the evolution in non-Markovian environments. For common reservoirs, a maximum creation of quantum correlations may occur under an appropriate temperature. For independent reservoirs, the non-Markovianity of the total system corresponds to the subsystem whose temperature is higher. In both common and independent environments, the Gaussian quantum discord is influenced by the temperature and the photon number of each mode.
How the prepared states and Unruh effect affect Measurement-Induced-Nonlocality (MIN) is studied. We show that, as the Unruh temperature increases, the MIN between modes A\mathrm{A}A and I\mathrm{I}I decreases but the MIN between modes A\mathrm{A}A and II\mathrm{II}II increases. We prove that the parameters cic_ici​ which decide initial prepared states affect not only the values of the MIN, but also the dynamical behavior of it. By comparing the MIN with the maximal expectation values of CHSH inequality and geometric discord between modes A\mathrm{A}A and I\mathrm{I}I, we also find that the MIN is more general than the quantum nonlocality related to violation of Bell's inequalities, and its values is always equal or bigger than that of the geometric 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.