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Communications in Theoretical Physics

Non-locality of Entangled Coherent States and Its Evolution in a Thermal Reservoir

Gong Ren-shan

Published Mar 1, 2005• 0 citations
Publisher

Abstract

Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for non-locality of entangled states, we present a perturbative calculation determining non-locality of evolving entangled states. Furthermore, by means of the perturbative calculation, the non-locality and its evolution of two kinds of entangled coherent states in a thermal reservoir are discussed.

DOI
10.1088/0253-6102/43/3/007

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Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for non-locality of entangled states, we present a perturbative calculation determining non-locality of evolving entangled states. Furthermore, by means of the perturbative calculation, the non-locality and its evolution of two kinds of entangled coherent states in a thermal reservoir are discussed.
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.
Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of 'non-locality breaking', which is defined in a natural way but within the purview of CHSH non-locality. This also provides a different perspective on the relationship between entanglement and non-locality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking, it is sufficient to 'break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breaking such a property does not hold in general, although for certain channels and for a restricted class of states for all channels this holds. We also consider channels whose output remains local under SLOCC and call them 'strongly non-locality breaking'. We provide a closed-form necessary-sufficient condition for any two-qubit state to show hidden CHSH non-locality, which is likely to be useful for other purposes as well. This in turn allows us to characterize all strongly non-locality breaking qubit channels. It turns out that unital qubit channels breaking non-locality of maximally entangled states are strongly non-locality breaking while extremal qubit channels cannot be so unless they are entanglement breaking.
We investigate how nonlocal entanglement, as identified by violations of a Bell inequality, may be protected during the evolution. Our system consists of two qubits each embedded in a bosonic reservoir evolving independently and initially in an entangled mixed state. We show that the violation of the Bell inequality can be related to the single-qubit population of excited state in such a way that, by appropriately choosing structured environments that give rise to sufficiently high values of population trapping, long-time protection of nonlocal entanglement can be correspondingly achieved.
Abstract Non-locality is a feature of quantum mechanics that cannot be explained by local realistic theory. It can be detected by the violation of Bell’s inequality. In this work, we have considered the evaluation of Bell’s inequality with the help of the XOR game. In the XOR game, a two-qubit entangled state is shared between the two distant players. It may generate a non-local correlation between the players which contributes to the maximum probability of winning of the game. We have aimed to determine the strength of the non-locality through XOR game. Thus, we have defined a quantity S NL called the strength of non-locality, purely on the basis of the maximum probability of winning of the XOR game. We have also derived the relation between the introduced quantity S NL and the quantity M introduced in [R Horodecki, P Horodecki, and M Horodecki, (1995) Phys. Lett. A 200, 340.], to study the non-locality of a two-qubit entangled state problem in depth. The quantity M may be defined as the sum of the two largest eigenvalues of the correlation matrix of the given entangled state and it determines whether the given entangled state under probe is non-local. Further, we have explored the non-locality of any two-qubit entangled state, whose non-locality cannot be detected by the CHSH inequality. Interestingly, we have found that the newly defined quantity S NL fails to detect non-locality for the entangled state, when the witness operator corresponding to CHSH operator cannot detect the entangled state. To overcome this problem, we have modified the definition of the strength of non-locality and have shown that the modified definition may detect the non-locality of such entangled states, which were earlier undetected by S NL . Furthermore, we have provided two applications of the strength S NL of the non-locality such as (i) establishment of a link between the two-qubit non-locality determined by S NL and the three-qubit non-locality determined by the Svetlichny operator and (ii) determination of the upper bound of the power of the controller in terms of S NL in controlled quantum teleportation.