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arXiv:1510.00119

Dilapidation of nonlocal correlations of two qubit states in noisy environment

K. G. Paulson, S. V. M. Satyanarayana

Published Oct 1, 2015• 0 citations
arXivHTMLPDF

Abstract

Composite quantum systems exhibit non-local correlations. These counter intuitive correlations form a resource for quantum information processing and quantum computation. In our previous work on two qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportaion, states that violate Bell-CHSH inequality and states that do not admit local hidden variable description is the hierarchy in terms of the order of nonlocal correlations. In order to establish this hierarchy, in the present work, we investigate the effect of noise on two quibt states that exhibit higher order nonlocal correlations. We find that dilapidation of nonlocal correlations in the presence of noise follow the same hierarchy, that is, higher order nonlocal correlation disappears for small strength of noise, where as lower order nonlocal correlations survive strong noisy environment. We show the results for decoherence due to amplitude damping channel on various quantum states. However, we observe that same hierarchy is followed by states undergoing decoherence due to phase damping as well as depolarizing channels.

DOI
10.48550/arxiv.1510.00119

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Composite quantum systems exhibit non-local correlations. These counter intuitive correlations form a resource for quantum information processing and quantum computation. In our previous work on two qubit maximally entangled mixed states, we observed that entangled states, states that can be used for quantum teleportaion, states that violate Bell-CHSH inequality and states that do not admit local hidden variable description is the hierarchy in terms of the order of nonlocal correlations. In order to establish this hierarchy, in the present work, we investigate the effect of noise on two quibt states that exhibit higher order nonlocal correlations. We find that dilapidation of nonlocal correlations in the presence of noise follow the same hierarchy, that is, higher order nonlocal correlation disappears for small strength of noise, where as lower order nonlocal correlations survive strong noisy environment. We show the results for decoherence due to amplitude damping channel on various quantum states. However, we observe that same hierarchy is followed by states undergoing decoherence due to phase damping as well as depolarizing channels.
We systematically characterize quantum entanglement in all sixteen combinations of two-qubit Bell states across three operational regimes: pure superposition, noiseless mixing, and asymmetric mixing of one noisy and one pure Bell state. For pure superpositions, we calculate the von Neumann entropy and show that entanglement depends critically on the relative phase phi between superposed states. For mixed states, we use concurrence C under three physically motivated decoherence channels. The Depolarizing (DP) and Phase Damping (PD) channels are modeled as global, collective operations on the two-qubit Hilbert space, while Amplitude Damping (AD) is treated as independent local decay on each qubit, reflecting the asymmetric, energy-dissipating nature of spontaneous emission. A central and counterintuitive result is that increasing noise can raise concurrence in specific parameter regimes across all three channels. We further map the boundary between mathematical entanglement (C > 0) and operational quantum non-locality using the Horodecki criterion, finding this boundary to be strongly channel-dependent. Under Phase Damping, the Bell-local entanglement regime vanishes entirely for identical and same-bases mixtures, meaning any surviving entanglement guarantees a CHSH violation. Under Depolarizing noise, a large Bell-local region requires mixing probability r > 1/sqrt(2) to recover non-locality at maximum noise. For Amplitude Damping, certain mixtures exhibit a non-monotonic Horodecki parameter M(T): concurrence decreases monotonically with noise, yet the capacity for CHSH violation is lost at intermediate noise levels and restored at high noise, as maximal damping repurifies the noisy branch. These results provide a unified analytical reference for entanglement and non-locality management across Bell-state combinations and decoherence channels relevant to NISQ architectures.
Consider a two-qubit maximally entangled state that gets corrupted when only one of the qubits is subjected to local interaction with the environment via amplitude damping channel. We show there are situations where this corrupted state gets better by allowing the other qubit also to interact with the environment. Moreover if the corrupted state is non teleporting, then it can always be made teleporting by the same prescription i.e. by allowing the second qubit to interact with the environment. Quantum entanglement [1] is a property of composite systems by virtue of which the local subsystems exhibit certain correlations among themselves that cannot be explained in classical terms. Often termed as quantum nonlocality, the subject had been under extensive study and debate since 1935 when Einstein, Podolsky and Rosen questioned the completeness of quantum mechanics [2]. Later, in 1964 in his pioneering work John Bell [3] showed that the correlations exhibited by the local subsystems that may be far apart are inherently quantum mechanical and any model admitting the description of local hidden variables (or one may prefer to say local realism) fails to explain such correlations.
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.
Abstract It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation. We study the decoherence of two remote qubits under general local single- and two-sided amplitude-damping channel (ADC). By using concurrence, quantum discord and Clauser–Horne–Shimony–Holt (CHSH) inequality, we find that the relation between the residual quantum correlations and the initial ones are different. Recently, Wang et al. [Int. J. Theor. Phys. 54 (2015) 5] showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction and quantum discord, respectively. Here we find that both in single- and two-sided ADC, only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality. That means the initial state with maximally nonlocality will retain its role in the evolution. It implies that the evolution of nonlocality may reveal the characteristics of quantum state better. Furthermore, we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel (GADC) and find that they are all proportional to that of the initial state.
We study the nonlocal properties of two-qubit maximally entangled and NNN-qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bell-inequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications of these anomalies on the usefulness of noisy Greenberger-Horne-Zeilinger states as resources for nonlocality-based physical protocols given by communication complexity problems.
Different nonlocal quantum correlations of entanglement, steering and Bell nonlocality are defined with the help of local hidden state and local hidden variable models. Considering their unique roles in quantum information processing, it is of importance to understand the individual nonlocal quantum correlation as well as their relationship. Here, we investigate the effects of amplitude damping decoherence on different nonlocal quantum correlations. In particular, we have theoretically and experimentally shown that the entanglement sudden death phenomenon is distinct from those of steering and Bell nonlocality. In our scenario, we found that all the initial states present sudden death of steering and Bell nonlocality, while only some of the states show entanglement sudden death. These results suggest that the environmental effect can be different for different nonlocal quantum correlations and, thus, it provides distinct operational interpretations of different quantum correlations.