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arXiv:1210.5291 · The Journal of Chemical Physics

Non-Markovianity and Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality violation in quantum dissipative systems

A. Thilagam, A. R. Usha Devi

Published Dec 4, 2012• 6 citations
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Abstract

We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay rate, λ(c) for select partitions. We discuss the applicability of these results to photosynthetic systems.

DOI
10.1063/1.4768045

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We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay rate, λ(c) for select partitions. We discuss the applicability of these results to photosynthetic systems.
We examine the non-Markovian dynamics in a multipartite system of two initially correlated atomic qubits, each located in a single-mode leaky cavity and interacting with its own bosonic reservoir. We show the dominance of non-Markovian features, as quantified by the difference in fidelity of the evolved system with its density matrix at an earlier time, in three specific two-qubit partitions associated with the cavity-cavity and atom-reservoir density matrices within the same subsystem, and the cavity-reservoir reduced matrix across the two subsystems. The non-Markovianity in the cavity-cavity subsystem is seen to be optimized in the vicinity of the exceptional point. The Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality computed for various two-qubit partitions show that high non-locality present in a specific subsystem appears in conjunction with enhanced non-Markovian dynamics in adjacent subsystems. This is in contrast to the matching existence of non-locality and quantum correlations in regions spanned by time t and the cavity decay rate, λc for select partitions. We discuss the applicability of these results to photosynthetic systems. © 2012 American Institute of Physics.
In this paper, we explore the dynamics of nonlocal correlations in a two-qubit system, that is, first prepared in a Gisin state and then interacts with a bosonic non-Markovian environment. We employ uncertainty-induced nonlocality (UIN) and the Horodecki measure (Bell function) to characterize the degree of nonclassical correlations and quantum nonlocality in the system, taking into account the influence of the non-Markovian reservoir. The dynamics of the UIN and the Bell nonlocality are next examined using the various parameters that define the non-Markovian reservoir and the initial Gisin state. Our results show that the amount of nonlocal correlations and the degree of violation of Bell’s inequality can be modulated by varying the physical parameters characterizing the non-Markovian reservoir and the initial Gisin state. We also show that in some specific cases, the system exhibits nonclassical correlations while the evolved Gisin state does not violate Bell’s inequality. Our results also confirm that UIN is robust than Bell’s nonlocality in the presence of decoherence induced by the interaction with the non-Markovian reservoir.
We evaluate the maximal Clauser-Horne-Shimony-Holt (CHSH) violation for a generic (typically mixed) qubit-qudit state, obtaining easily computable expressions in arbitrary qudit dimension. This represents the optimal (2-2-2) Bell nonlocality for this kind of systems. The work generalizes the well-known Horodeckis result for a qubit-qubit setup. We also give simple lower and upper bounds on that violation. We apply our general results to address a number of issues, namely, we obtain a bound on the degree of purity required in a system to exhibit nonlocality and study the statistics of nonlocality in random density matrices. In addition, we show the impossibility of improving the amount of CHSH violation by embedding the qudit in a Hilbert space of larger dimension. Finally, the general result is illustrated with a family of density matrices in the context of a qubit-qutrit system.
We revisit the generation and evolution of Bell nonlocality in hybrid scenarios of which the dynamics is determined by the Jaynes-Cummings Hamiltonian, a relevant example of which is the atom-cavity system. Previous approaches evaluate the nonlocality through the well-known qubit-qubit Clauser-Horne-Shimony-Holt (CHSH) formulas, using combinations of pseudospin operators for the electromagnetic (EM) field observables. While such an approach is sensible, it is far from optimal. In the present work we have used recent results on optimal Bell violation in qubit-qudit systems, showing that the nonlocality is much greater than previously estimated, both with and without noise. In addition, we provide an optimal treatment of noise, ensuring that our results are the best possible within this framework. We illustrate the results using different initial states for the EM field, including squeezed and coherent states. In addition, we study the asymptotic behavior of the entanglement. Remarkably, starting with a generic separable pure coherent state, the asymptotic mixed state is entangled, though it does not violate CHSH inequalities.
We examine the Zeno and anti-Zeno effects in the context of non-Markovian dynamics in entangled spin-boson systems in contact with noninteracting reservoirs. We identify enhanced non-Markovian signatures in specific two-qubit partitions of a Bell-like initial state, with results showing that the intra-qubit Zeno effect or anti-Zeno effect occurs in conjunction with inter-qubit non-Markovian dynamics for a range of system parameters. The time domain of effective Zeno or anti-Zeno dynamics is about the same order of magnitude as the non-Markovian time scale of the reservoir correlation dynamics, and changes in decay rate due to the Zeno mechanism appears coordinated with information flow between specific two-qubit partitions. We extend our analysis to examine the Zeno mechanism-non-Markovianity link using the tripartite states arising from a donor-acceptor-sink model of photosynthetic biosystems.
Abstract We investigate the Bell nonlocality dynamics of bipartite quantum systems under three distinct types of global decoherence environments: global amplitude damping noise, globally correlated classical noise, and global phase-damping noise. By combining numerical optimization techniques over Bell inequalities—specifically the Clauser–Horne–Shimony–Holt inequality—and describing the global noise-evolution process of a two-qubit system with the Kraus operator formalism, we systematically characterize the evolution of quantum nonlocality in a two-qubit system. Our results demonstrate that, under a global amplitude damping noise environment, precise temporal modulation of the amplitude damping channel enables the composite system to retain maximal Bell-nonlocal correlations in its final state. In contrast, globally correlated classical noise fields induce exponential suppression of Bell inequality violations. Remarkably, the systems subjected to global phase-damping noise exhibit pronounced robustness to nonlocality. These findings highlight the critical role of global noise in nonlocality dynamics.