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Fluctuation and Noise Letters

The Dynamics of Three Different Entropic Measures of Quantum Correlations in Mixed Bipartite State Coupled with Classical Environments

Mahmood Shamirzaie, Salman Khan

Published May 13, 2018• 7 citations
Publisher

Abstract

The dynamics of three different entropic measures of quantum correlations in mixed bipartite qubit states in the presence of two different classical noises, the static noise (SN) and the random telegraph noise (RTN), are investigated. The three entropic measures of quantum correlations correspond to one-way information deficit, geometric quantum discord and the cubic information. General analytic relations for each quantifier in the two configurations are obtained. In both configurations, the minimized value of each measure of quantum correlations corresponds to the conditional entropy of the same projectors. It is shown that one-way information deficit captures more correlations in highly mixed initial states. On the contrary, in both configurations the cubic information reduces to the geometric quantum discord and captures more correlations for highly pure initial states. The periodic revival of each measure of quantum correlation is more prominent in the case of RTN.

DOI
10.1142/s0219477518500232

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The dynamics of three different entropic measures of quantum correlations in mixed bipartite qubit states in the presence of two different classical noises, the static noise (SN) and the random telegraph noise (RTN), are investigated. The three entropic measures of quantum correlations correspond to one-way information deficit, geometric quantum discord and the cubic information. General analytic relations for each quantifier in the two configurations are obtained. In both configurations, the minimized value of each measure of quantum correlations corresponds to the conditional entropy of the same projectors. It is shown that one-way information deficit captures more correlations in highly mixed initial states. On the contrary, in both configurations the cubic information reduces to the geometric quantum discord and captures more correlations for highly pure initial states. The periodic revival of each measure of quantum correlation is more prominent in the case of RTN.
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.
In the present paper, the joint effects of two kinds of classical environmental noises, without direct interaction among each other, on the dynamics of quantum correlations (QCs) of a three-qubit system coupled in independent environments is investigated. More precisely, we join the random telegraph noise (RTN) and the static noise (SN) and focus on the dynamics of entanglement and quantum discord (QD) when the qubits are initially prepared in the GHZ- and W-type states. The overall noise affecting the qubits is obtained by combining the RTN and SN in two different setups. The results show that the disorder of the environmental noise as well as its memory qualities and the purity of the initial state considered play a crucial role in the time evolution of the system in such a way that the dynamics of QCs can be controlled by varying them. In fact, we show that, depending on the initial state and noise regime considered, the rate of collapse of QCs may either decrease or increase with the increase of the degree of disorder of the SN, the switching rate of the RTN and the purity of the initial state.
Abstract The dynamics of one-way information deficit, geometric quantum discord and quantum coherence in mixed bipartite qubit state in the presence of classical colored noise with 1/ f α spectrum are investigated. The source of the noise spectrum is a single fluctuator with undetermined switching rate. The analysis is made under the frame work of collective coupling between the components of the system and environment. Qualitatively the responses of all the three quantities are similar to the noise, however, quantum coherence stands robust than the other two quantities. Depending on choice of the different regimes of the characteristic parameters of the noise, the decay in all the three quantities can be monotonic, damped oscillating or exhibiting sudden death with revivals.
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 XXX states and the mixture of two aligned states.
Abstract We address the dynamics of the lower bound of geometric quantum discord and quantum-memory-assisted entropic uncertainty in a two-qutrit system when exposed to classical channels characterized by power-law (PL) and random telegraph (RT) noises. The system-channel coupling strategy is examined in two contexts: common qutrit-environment (CQE) and different qutrit-environment (DQE) configurations. We show that the geometric quantum discord functions remain anti-correlated with entropic uncertainty and decline as uncertainty appears in the system. The rate of entropic uncertainty appearance seems more prevalent than the decline rate of quantum discord function, suggesting that uncertainty causes the quantum correlations to fade in quantum systems. We find that non-local correlations estimated by the lower bound of geometric quantum discord are not destroyed even at the maximum entropic disorder and entropic uncertainty. In addition, the efficacy of entropic uncertainty and the lower bound is strongly influenced by the state’s purity factor, with the former being more robust at higher purity values and the latter at lower purity values. All the parameters impact entropic uncertainty, however, the mixedness of the state is noticed to greatly alter the generation of quantum memory. Besides, PL noise caused Markovian behavioral dynamics, and the RT noise allowed non-Markovian dynamics, while the latter remains more resourceful for the quantum correlations preservation and entropic uncertainty suppression. We also demonstrate how to model longer quantum correlations and provide optimal parameter settings for suppressing the dephasing and entropic uncertainty effects.
We analyze the dynamics of both entanglement and quantum discord (QD) in a system of two non-interacting flux-qubits initially prepared in a Bell's state and subjected to either static or random telegraph noises (RTNs). Both independent and common sources of system-environment coupling are considered either in the Markovian or non-Markovian regime and the results are compared to those of ordinary qubits. Under suitable conditions, both entanglement and QD are more robust in flux-qubit systems than classical ones. In the Markovian regime where the decay is monotonic, they are both stronger in different environment coupling than in common coupling, while the opposite is found in the non-Markovian regime where the dynamics is stressed by sudden death and revival phenomena, more robust in qubits than in flux-qubits under dynamical RTN. Weakness of revival amplitudes is interpreted as a noise spectrum-related induced interaction affecting quantum features of the system, while energy level non-degeneracy (at zero-splitting) of flux-qubits induces a phase factor that set conditions under which entangled states can be experimentally witnessed in flux-qubit systems. Note that the energy levels non-degeneracy has no particular effect on other entanglement measures apart from entanglement witnesses.