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理论物理通讯：英文版

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

GONGRen-Shan

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for nonlocality 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.

Related papers

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

Gong Ren-shan

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.

Communications in Theoretical Physics•Mar 1, 2005•0 citations

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By using Bell CHSH inequality,nonlocality of a kind of entangled coherent state and its evolution in a vacuum thermal reservoir are studied.It is shown that nonlocality of the state are related with the phases.In this paper we just give the results when φ-2=0 is satisfied,on the other hand nonlocality of the state decreases gradually and disappears finally under the time evolution in a vacuum thermal reservoir.

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Gong Ren-shan

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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Non-locality breaking qubit channels: the case for CHSH inequality

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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.

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Quantum Entanglement and Nonlocality Properties of Two-Mode Squeezed Thermal States in a Common-Reservoir Model

Shao-Hua Xiang, Kehui Song, Wei Wen +1 more

We study a system consisting of two identical non-interacting single-mode cavity fields coupled to a common vacuum environment and provide general, explicit, and exact solutions to its master equation by means of the characteristic function method. We analyze the entanglement dynamics of two-mode squeezed thermal state in this model and show that its entanglement dynamics is strongly determined by the two-mode squeezing parameter and the purity. In particular, we find that two-mode squeezed thermal state with the squeezing parameter is extremely fragile and almost does not survive in a common vacuum environment. We investigate the time evolution of nonlocality for two-mode squeezed thermal state in such an environment. It is found that the evolved state loses its nonlocality in the beginning of the evolution, but after a time, the revival of nonlocality can occur.

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Strength of the non-locality of two-qubit entangled states and its applications

Anuma Garg, Satyabrata Adhikari

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.

arXiv:2212.10885•Physica Scripta•Mar 24, 2023•2 citations
Regarding the necessary and sufficient condition violating Bell-CHSH's inequality as criterion for nonlocality 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 study a system consisting of two identical non-interacting single-mode cavity fields coupled to a common vacuum environment and provide general, explicit, and exact solutions to its master equation by means of the characteristic function method. We analyze the entanglement dynamics of two-mode squeezed thermal state in this model and show that its entanglement dynamics is strongly determined by the two-mode squeezing parameter and the purity. In particular, we find that two-mode squeezed thermal state with the squeezing parameter is extremely fragile and almost does not survive in a common vacuum environment. We investigate the time evolution of nonlocality for two-mode squeezed thermal state in such an environment. It is found that the evolved state loses its nonlocality in the beginning of the evolution, but after a time, the revival of nonlocality can occur.
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.