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Chinese Physics B

Tripartite states Bell-nonlocality sudden death in a quantum-critical environment

Deng-Yu Zhang, Xie Li-Jun, Shi-Qing Tang, Zhan Xiao-Gui, Yinhua Chen, Gao Feng

Published Oct 1, 2010• 3 citations
Publisher

Abstract

We demonstrate that multipartite Bell-inequalities violations can be fully destroyed in finite time in three-qubit states under a quantum-critical environment, which is an Ising model in a transverse field. We use the Mermin-Ardehali—Belinksii—Klyshko (MABK) inequality to detect the degree of nonlocality as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of environment and the strength of transverse field on the Bell-inequality violations are given for two different initial states, namely, the W class and GHZ class states. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by the decoherence under certain conditions.

DOI
10.1088/1674-1056/19/10/100305

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We demonstrate that multipartite Bell-inequalities violations can be fully destroyed in finite time in three-qubit states under a quantum-critical environment, which is an Ising model in a transverse field. We use the Mermin-Ardehali—Belinksii—Klyshko (MABK) inequality to detect the degree of nonlocality as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of environment and the strength of transverse field on the Bell-inequality violations are given for two different initial states, namely, the W class and GHZ class states. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by the decoherence under certain conditions.
This paper demonstrates that multipartite Bell-inequality violations can be fully destroyed in a finite time in three-qubit states coupled to a general XY spin-chain with a three-site interaction environment. The Mermin—Ardehali—Belinksii—Klyshko inequality is used to detect the degree of nonlocality, as measured by the extent of their violations. The effects of system-environment couplings, the size of degrees of freedom of the environment and the strength of the three-site interaction on the Bell-inequality violations are given. The results indicate that the Bell-inequality violations of the tripartite states will be completely destroyed by decoherence under certain conditions for the GHZ state. The decoherence-free subspaces of our model are identified and the entanglement of quantum states is also discussed.
We investigate the entanglement dynamics of three-qubit states in a quantum-critical environment, which is an Ising model in a transverse field. By using negativity as entanglement measure, we find that the entanglement evolution depends not only on the system-environment couplings and the size of degrees of freedom of environment but also on the strength of transverse field and the symmetry of quantum states of concern. In particular, for the cases under study, our results imply that the entanglement decay can be enhanced by the quantum phase transition of the environment under weak coupling. Our analysis implies that the entanglement of any three-qubit quantum state will be completely destroyed by the decoherence under certain conditions, that we detail below.
We study the Bell-nonlocality dynamics of three remote atoms, two of which are trapped in one single-mode cavity and the third atom is trapped in another remote single-mode cavity. The interactions between the atoms and the cavity modes are studied via Tavis Cummings and Jaynes Cummings models. Here, the two single-mode cavities are introduced to simulate two different enviroments of the three atoms. The tripartite nonlocal correlations are studied in terms of the Svetlichny inequality and the WWZB inequality, respectively. The results show that the tripartite Bell-nonlocality sudden death will occur for the W state and GHZ state initial conditions. The detailed results demonstrate that the tripartite nonlocality of GHZ state is more robust than that of W state when suffering from the effect of environments.
We study the nonlocality dynamics for an eight-qubit model in cavity QED, where four atoms are confined in four different cavities, all of them initially prepared in the maximally correlated state of four qubits, which corresponds to the atomic degrees of freedom. The nonlocality evolution for the latter states will show that the corresponding maximal violation of a multipartite Bell inequality will experience revivals at precise times, defining, in analogy with entanglement, nonlocality sudden deaths, as well as nonlocality sudden rebirths. The present contribution paves the way to describe, by employing the nonlocality multipartite correlation measure, collective complex behavior displayed by slightly interacting cavity QED arrays.