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Scientific Reports

The dynamic behaviors of complementary correlations under decoherence channels

Ming‐Ming Du, Dong Wang, Liu Ye

Published Jan 30, 2017• 7 citations
Publisher

Abstract

Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here, we explore an effective method to identify the entangled Bell diagonal states by means of Pearson correlation, one of the complementary correlations. Then, we extend this method to expose the dynamic behavior of complementary correlations under various kinds of decoherence channels. The sudden death and revival of entanglement can be explained by the idea of Pearson correlation. The threshold that is used to identify entanglement is proposed. Furthermore, we put forward a new method to expound the underlying physical mechanisms for which classical and quantum correlations suffer a sudden change in the decoherence process.

DOI
10.1038/srep40934

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Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here, we explore an effective method to identify the entangled Bell diagonal states by means of Pearson correlation, one of the complementary correlations. Then, we extend this method to expose the dynamic behavior of complementary correlations under various kinds of decoherence channels. The sudden death and revival of entanglement can be explained by the idea of Pearson correlation. The threshold that is used to identify entanglement is proposed. Furthermore, we put forward a new method to expound the underlying physical mechanisms for which classical and quantum correlations suffer a sudden change in the decoherence process.
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Quantum correlation lies at the very heart of almost all the non-classical phenomena exhibited by quantum systems composed of more than one subsystem. In the recent days it has been pointed out that there exists quantum correlation, namely discord which is more general than entanglement. Some authors have investigated that for certain initial states the quantum correlations as well as classical correlation exhibit sudden change under simple Markovian noise. We show that, this dynamical behavior of the both types of correlations can be explained using the idea of complementary correlations introduced in [arXiv:1408.6851]. We also show that though certain class of mixed entangled states can resist the monotonic decay of quantum correlations,it is not true for all mixed states. Moreover, pure entangled states of two qubits will never exhibit such sudden change.
Manipulating dynamical evolution is an important task in quantum information. The sudden death phenomenon (SDP), which is predicted to be unattainable beyond entanglement [T. Yu and J. H. Eberly, Sudden death of entanglement, Science 323, 598 (2009)], would be an especially surprising feature in quantum coherence. In this paper, we modulate the spatial modes of photons and build a spatially inclined channel using a series of specially made quartz plate pairs. Within this channel, sudden changes in coherence occur in open-quantum systems. We, then, describe the SDP within a general theoretical framework of sudden quantum-coherence changes and by defining the nthn\mathrm{th}nth-order sudden coherence change. Moreover, by adding non-Markovian noise, we find that coherence can rebirth after a sudden death. We further compare the sudden change features in coherence and quantum entanglement. We find that both coherence and entanglement perform identical dynamical processes upon Bell diagonal states, although their dynamical characteristics change when the initial state is partially entangled. Our results provide insights into the sudden change phenomena of quantum correlations beyond entanglement along with intriguing perspectives on quantum coherence dynamics.
We investigate the dynamics of correlations for two-parameter qubit-qutrit states under various local decoherence channels including depahsing, phase-flip, bit- and trit-flip, bit- and trit-phase-flip, and depolarizing channels. We find that, under certain conditions, the classical correlations may not be affected by the noise or decay monotonically. The quantum correlations measured by measurement-induced disturbance (MID) show three types of dynamical behaviors: (i) monotonic decay to zero, (ii) monotonic decay to a nonzero steady value, (iii) increase from zero and then decrease to zero in a monotonic way. Consequently, we find that, differing from the dynamics of entanglement, the present classical and quantum correlations do not reveal sudden death behavior.
We experimentally investigate the dynamics of classical and quantum correlations of a Bell diagonal state in a non-Markovian dephasing environment. The sudden transition from a classical to a quantum decoherence regime is observed during the dynamics of a Bell diagonal state. Due to the refocusing effect of the overall relative phase, the quantum correlation revives from near zero and then decays again in the subsequent evolution. However, the non-Markovian effect is too weak to revive the classical correlation, which remains constant in the same evolution range. With the implementation of an optical ${\ensuremath{\sigma}}_{x}$ operation, the sudden transition from a quantum to a classical revival regime is obtained, and correlation echoes are formed. Our method can be used to control the revival time of correlations, which would be important in quantum memory.
Complementary correlations can reveal the genuine quantum correlations present in a composite quantum system. Here we investigate the relation between complementary correlations and other aspects of genuine quantum correlations. We show that for a certain class of states quantum correlations revealed through complementary correlations become equal to entanglement and discord. We also provide a necessary and sufficient condition for entanglement distribution with separable Bell diagonal states in terms of complementary correlations.