Entanglement Measure and Quantum Violation of Bell-Type Inequality

Ding, Dong; He, Ying-Qiu; Yan, Fei; Gao, Ting

doi:10.1007/s10773-016-3048-1

Cited by 9 publications

(4 citation statements)

References 60 publications

(64 reference statements)

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“…( , we obtain similar equation of (9). We only need to consider the case |φ 3|12 ⟩ = t 0 |000⟩ + t 1 |101⟩ + t 2 |210⟩.…”

Section: And Thus Tr(amentioning

confidence: 66%

“…There have been many important generalizations and interesting applications of Bell inequalities [6][7][8]. By calculating the measures of entanglement and the quantum violation of the Bell-type inequality, a relationship between the entanglement measure and the amount of quantum violation was derived in [9]. However, for high-dimensional multiple quantum systems the results for such relationships between the entanglement and the nonlocal violation are still far from being satisfied.…”

Section: Introductionmentioning

confidence: 99%

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A note on entanglement classification for tripartite mixed states

2022

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We study the classification of entanglement in tripartite systems by using Bell-type inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell inequalities which classifies the entanglement of triqutrit fully separable and bi-separable mixed states. By using the correlation tensors in the principal basis representation of density matrices, we obtain separability criteria for fully separable and bi-separable 2 ⊗ 2 ⊗ 3 quantum mixed states. Detailed example is given to illustrate our criteria in classifying the tripartite entanglement.

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“…( , we obtain similar equation of (9). We only need to consider the case |φ 3|12 ⟩ = t 0 |000⟩ + t 1 |101⟩ + t 2 |210⟩.…”

Section: And Thus Tr(amentioning

confidence: 66%

Section: Introductionmentioning

confidence: 99%

A note on entanglement classification for tripartite mixed states

2022

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“…Quantum entanglement has received extensive attention, and many results have been obtained [1][2][3]. Since entangled states violate Bell type inequalities, so they are nonlocal [4][5][6][7][8][9][10][11]. However, in 1999, Bennett et al [12] proposed a complete orthogonal product bases with nonlocality, i.e., each of which cannot be reliably discriminated by local operations and classical communication (LOCC) while it only can be identified by a global measurement.…”

Section: Introductionmentioning

confidence: 99%

On orthogonal product sets with strong quantum nonlocality on plane structure

Zhou¹,

Gao²,

Yan³

2022

Preprint

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In this paper, we consider the orthogonal product set (OPS) with strong quantum nonlocality. Based on the decomposition of plane geometry, we present a sufficient condition for the triviality of orthogonality-preserving POVM on fixed subsystem and partially answer an open question given by Yuan et al. [Phys. Rev. A 102, 042228 (2020)]. The connection between the nonlocality and the plane structure of OPS is established. We successfully construct a strongly nonlocal OPS indA, dB, dC ≥ 4), which contains fewer quantum states, and generalize the structures of known OPSs to any possible three and four-partite systems. In addition, we present several entanglement-assisted protocols for perfectly local discrimination the sets. It is shown that the protocols without teleportation use less entanglement resources on average and these sets can always be discriminated locally with multiple copies of 2-qubit maximally entangled states. These results also exhibit nontrivial signification of maximally entangled states in the local discrimination of quantum states.

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“…Over the past few years, scholars have intensively studied the relationship between entanglement and Bell nonlocality [10,37,[47][48][49][50][51], the relationship between quantum discord and GMQD [26,31], the relationship between entanglement and quantum discord [52], and the relationship between Bell nonlocality and GMQD [28,45]. Some scholars have also compared three of the four quantum correlation dynamics [53][54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Dynamic behavior of the quantum correlations of two cavity fields in the double Jaynes–Cummings model

Liu¹,

Wang²,

Zheng³

et al. 2022

Laser Phys. Lett.

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The influence of the atom’s spatial degrees of freedom and the purity of the initial state on the dynamics of Bell non-locality, entanglement, geometric measure of quantum discord (GMQD) and quantum discord in a double Jaynes–Cummings model are investigated. We study the above four quantum correlations for an initial Werner-like state between the electronic states of the two atoms and between the two cavities respectively and find that all these quantum correlations are sensitive to the wave packet width and the purity of the initial state. For Bell non-locality, we find the phenomenon of sudden death and sudden birth, whereas the other three quantum correlations decay to zero asymptotically. We find that both the wave packet width and the purity of the initial state affect the GMQD and quantum discord in a similar way and we also notice that GMQD and quantum discord always exist, except where the purity of the initial state is zero, while Bell non-locality and entanglement can occur only when the purity meets certain conditions.

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Entanglement Measure and Quantum Violation of Bell-Type Inequality

Cited by 9 publications

References 60 publications

A note on entanglement classification for tripartite mixed states

A note on entanglement classification for tripartite mixed states

On orthogonal product sets with strong quantum nonlocality on plane structure

Dynamic behavior of the quantum correlations of two cavity fields in the double Jaynes–Cummings model

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