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Journal of Nanchang University

ON THE NONLOCALITY OF TWO KINDS OF ENTANGLED COHERENT STATES

Gong Ren-shan

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

By using the criterion for violating Bell-CHSH inequality proposed by Horodecki,we have studied the quantum nonlocality of two kinds of entangled coherent states.Some formulas for evaluating the maximal expectation values of Bell-CHSH type operators of these entangled coherent states are derived.It is shown that the quantum nonlocality has relations with the strength and phase of coherent state.When some relations of the strength and phase are satisfied the nonlocality of entangled coherent states may disappear.

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By using the criterion for violating Bell-CHSH inequality proposed by Horodecki,we have studied the quantum nonlocality of two kinds of entangled coherent states.Some formulas for evaluating the maximal expectation values of Bell-CHSH type operators of these entangled coherent states are derived.It is shown that the quantum nonlocality has relations with the strength and phase of coherent state.When some relations of the strength and phase are satisfied the nonlocality of entangled coherent states may disappear.
We investigate the detection problem of quantum nonlocal correlation by two qubit detectors. The detectors with an initial product state interact with a massless scalar field in the vacuum state, and then the out-state of the detectors are correlated after the interaction. Under the perturbative treatment in the second order of the coupling, the detectors' state can be entangled but satisfies the Bell-CHSH inequality. It is known that the violation of the Bell-CHSH inequality for such an entangled state is obtained after a local filtering operation. In this paper, we construct the optimal filtering operation for the qubit detectors and derive the success probability of the filtering operation, which characterizes the reliability of revealing the Bell-CHSH nonlocality by the filtering operations. By applying the optimal filtering, it is shown that the detected Bell-CHSH nonlocality depends on the coherence of the detectors' state and the spontaneous emission of scalar particles from each detector. We also comment on a trade-off relation between the success probability and the size of the parameter region showing quantum correlation.
In two-mode interferometry, for a given total photon number N, entangled Fock state superpositions of the form (Formula presented.) have been considered for phase estimation. Indeed all such states are maximally mode-entangled and violate a Clauser–Horne–Shimony–Holt (CHSH) inequality. However, they differ in their optimal phase estimation capabilities as given by their quantum Fisher informations. The quantum Fisher information is the largest for the N00N state (Formula presented.) and decreases for the other states with decreasing photon number difference between the two modes. We ask the question whether for any particular Clauser–Horne (CH) (or CHSH) inequality, the maximal values of the CH (or the CHSH) functional for the states of the above type follow the same trend as their quantum Fisher informations, while also violating the classical bound whenever the states are capable of sub-shot-noise phase estimation, so that the violation can be used to quantify sub-shot-noise sensitivity. We explore CH and CHSH inequalities in a homodyne setup. Our results show that the amount of violation in those nonlocality tests may not be used to quantify sub-shot-noise sensitivity of the above states.
We investigate the nonlocality of Schmidt-correlated (SC) states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser—Horne—Shimony—Holt (CHSH) inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequality is only a sufficient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence, and relative entropy entanglement are discussed.
We investigate the nonlocality of Schmidt-correlated (SC) states, and present analytical expressions of the maximum violation value of Bell inequalities. It is shown that the violation of Clauser—Horne—Shimony—Holt (CHSH) inequality is necessary and sufficient for the nonlocality of two-qubit SC states, whereas the violation of the Svetlichny inequality is only a sufficient condition for the genuine nonlocality of three-qubit SC states. Furthermore, the relations among the maximum violation values, concurrence, and relative entropy entanglement are discussed.