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arXiv:1807.02342 · Canadian Journal of Physics

Invariant entanglement and generation of quantum correlations under global dephasing

Göktuğ Karpat

Published Dec 21, 2017• 2 citations
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Abstract

We investigate the dynamics of quantum entanglement and more general quantum correlations quantified via negativity and local quantum uncertainty, respectively, for two-qubit systems undergoing Markovian collective dephasing. Focusing on a two-parameter family of initial two-qubit density matrices, we study the relation of the emergence of the curious phenomenon of time-invariant entanglement and the dynamical behavior of local quantum uncertainty. Developing an illustrative geometric approach, we demonstrate the existence of distinct regions of quantum entanglement for the considered initial states and identify the region that allows for completely frozen entanglement throughout the dynamics, accompanied by generation of local quantum uncertainty. Furthermore, we present a systematic analysis of different dynamical behaviors of local quantum uncertainty, such as its sudden change or smooth amplification, in relation with the dynamics of entanglement.

DOI
10.1139/cjp-2017-0684

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We investigate both theoretically and experimentally the dynamics of entanglement and nonlocality for two qubits immersed in a global pure dephasing environment. We demonstrate the existence of a class of states for which entanglement is forever frozen during the dynamics, even if the state of the system does evolve. At the same time nonlocal correlations, quantified by the violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, either undergo sudden death or are trapped during the dynamics.
Most studies of collective dephasing for bipartite as well as multipartite quantum systems focus on a very specific orientation of magnetic field, that is, z-orientation. However, in practical situations, there are always small fluctuations in stochastic field and it is necessary that more general orientations of fields should be considered. We extend this problem to qubit-qutrit systems and study correlation dynamics for entanglement and local quantum uncertainty for some specific quantum states. We find that certain quantum states exhibit freezing dynamics both for entanglement and local quantum uncertainty. We analyze the asymptotic states and find the conditions for having non-zero entanglement and local quantum uncertainty. Our results are relevant for ion-trap experiments and can be verified with current experimental setups.
Abstract In this paper, we address the dynamics of nonclassical correlation, quantified by local quantum uncertainty (LQU) in a two-qubit system subjected to classical environmental noise when the initial states of system are prepared in a specific class of Bell states. Two different configurations of the local noisy environment are examined. In the first case, we consider a system of two independently qubits, each locally interacting with its classical random noise, whereas in the second case we consider only one of qubits subject to a classical random noise. Our results show that the dynamics of LQU is strongly related to both the dephasing and relaxation factors. The behaviors of LQU in above two cases exhibit similar variation, with monotonic decay in the weak coupling region, while revivals in the strong coupling region depending on the ratio of the switching rate and coupling strength to the qubit. By controlling this ratio, long-time survival of LQU is obtained. Therefore, our results may open an interesting perspective in using of the long-time survival of quantum correlations for practical applications in quantum information science.
We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo et al (2007 Phys. Rev. Lett. 99 160502). We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the |GHZ⟩ and | W ⟩ states, and compare their average behavior with the average behavior exhibited by initial maximally entangled two-qubit states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert–Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.
We investigate the dynamics of nonclassical correlations including concurrence and local quantum uncertainty in the damped Jaynes–Cummings model with an initial system–reservoir correlation. The dynamics of qubit–reservoir correlation and the influence of non-Markovian effect are studied. Furthermore, we consider the double damped Jaynes–Cummings model consisting of two noninteracting qubits locally coupled to independent reservoirs and explore the properties of both qubit–qubit and reservoir–reservoir correlations. The influences of initial correlation and non-Markovian effect on the dynamics of nonclassical correlations are analyzed. It is found that the dynamics for both qubit–qubit and reservoir–reservoir correlations can be significantly changed by the initial correlation and the non-Markovian effect. Finally, we explore the sudden changes of local quantum uncertainty and find that they are closely related to the initial system–environment entanglement.