Einstein-Podolsky-Rosen steering and coherence in the family of entangled three-qubit states

Kalaga, J. K.; Leoński, W.; Peřina, Jan

doi:10.1103/physreva.97.042110

Cited by 44 publications

(31 citation statements)

References 57 publications

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“…One can see that Corollary 4 reduces to the monogamy inequality (21), if k = 1 and 0 ≤ β = δ ≤ 1. Example 3.…”

Section: Polygamy Relations For General Quantum Correlationsmentioning

confidence: 99%

“…In [3][4][5], the authors have shown that the xth power of the entanglement of formation (x ≥ √ 2) and the concurrence (x ≥ 2) satisfy multiqubit monogamy inequalities. Monogamy relations for quantum steering have also been demonstrated in [17][18][19][20][21]. Later, polygamy inequalities were proposed in terms of the αth (0 ≤ α ≤ 1) power of square of convex-roof extended negativity (SCREN) and the entanglement of assistance [14,22].…”

Section: Introductionmentioning

confidence: 99%

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Complementary quantum correlations among multipartite systems

Jin

Fei

Qiao

2020

Quantum Inf Process

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We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems. General monogamy relations are presented for the αth (0 ≤ α ≤ γ, γ ≥ 2) power of quantum correlation, and general polygamy relations are given for the βth (β ≥ δ, 0 ≤ δ ≤ 1) power of quantum correlation. These monogamy and polygamy inequalities are complementary to the existing ones with different parameter regions of α and β. Applying these results to specific quantum correlations, the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given.

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“…One can see that Corollary 4 reduces to the monogamy inequality (21), if k = 1 and 0 ≤ β = δ ≤ 1. Example 3.…”

Section: Polygamy Relations For General Quantum Correlationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complementary quantum correlations among multipartite systems

Jin

Fei

Qiao

2020

Quantum Inf Process

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“…Specially, from Theorem 6 we have [Theorem 7]. For any multipartite state ρ AB0···BN−1 , if E aAB i ≤ N −1 j=i+1 E aAB j for all i = 0, 1, · · · N − 2, we have (N a scA|B 0 B1···BN−1 ) β ≤ N −1 j=0 (2 β − 1) j (N a scAB j ) β (26) for β ≥ 1. Example 4.…”

Section: Polygamy Relations For Screnoamentioning

confidence: 99%

“…(27) We have N a scA|B 1 B2B3 = 3 4 , N a scAB i = 1 4 , i = 1, 2, 3. Let y be the difference between the right and left hand of inequality (26). One has y = [2 β + (2 β − 1) 2 ]( 1 4 ) β − ( 3 4 ) β ; see Fig.…”

Section: Polygamy Relations For Screnoamentioning

confidence: 99%

Polygamy relations of multipartite systems

Jin

Fei

Qiao

2019

Quantum Inf Process

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“…Even though these QRs are playing different roles in different quantum‐information tasks, the intrinsic relations behind the QRs might be the same one. Recently, many researchers have made progress for this target . For example, Kalaga et al .…”

Section: Introductionmentioning

confidence: 99%

Intrinsic Relations of Bipartite Quantum Resources in Tripartite Systems

et al. 2018

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Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, the correlations of the tripartite W-type states based on bipartite quantum resources are investigated. The inter-relations among the degree of coherence, concurrence, Bell nonlocality, and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser-Horne-Shimony-Holt inequality) states for the two-qubit subsystems derived from the tripartite W-type states, exact lower and upper boundaries of the degree of coherence versus concurrence are obtained. Interestingly, exact relation among the degree of coherence, concurrence, and purity is obtained. Moreover, coherence is also closely related to entanglement in two specific scenarios: the tripartite W-type state under decoherence and a practical system for a renormalized spin-1/2 Heisenberg model. Entanglement, that serve as one of the most generally used QRs, is defined as the inseparability of quantum states and can be considered as an algebraic concept. [3] For entanglement measures, there are many mathematical measures methods, such as relative entropy of entanglement (REE), [10,11] entanglement of formation (EOF), [12] concurrence, [10,13] and negativity. [14,15] Here, the negativity is an entanglement cost measure under the positivity of partial transpose for quantum operations preserving. [14] It is wellknown that the concurrence of a quantum state can always exceed its negativity, and the REE is less than its EOF. [12] For bipartite pure states, the concurrence is exactly equivalent to its negativity. Besides, another one quantum resource can be discovered by violating some Bell-type inequalities, and is termed as Bell nonlocality. [16][17][18][19][20][21][22][23] One of these Bell-type inequalities, the Clauser-Horne-Shimony-Holt (CHSH) inequality [3][4][5] has been often considered as a measure for the QNCs presented between spatially separated two parties that are entangled, and thereby it can violate the bound originated by the inequality. [22] It is noteworthy that, Bell-type inequalities can be violated only if their states are entangled. However, there are entangled states that can still exhibit QNCs which cannot violate any Bell-type inequality for any possible local measurements proposed by Werner [24] in 1989. Then, the sufficient and necessary conditions for arbitrary bipartite states to be Bell nonlocal states were derived [25] in 1995. The last one is called as EPR steering, [6,7] which was introduced by Schrödinger [26] to analyze the EPR-paradox in 1935. Conceptually, EPR steering is able to describe that an observer can instantaneously affect a remote system by utilizing local measurements. In addition, EPR steering has been viewed as an intermediate type of quantum resource [27][28][29] between entanglement and Bell nonlocality in modern quantum-information theory. Except for t...

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Einstein-Podolsky-Rosen steering and coherence in the family of entangled three-qubit states

Cited by 44 publications

References 57 publications

Complementary quantum correlations among multipartite systems

Complementary quantum correlations among multipartite systems

Polygamy relations of multipartite systems

Intrinsic Relations of Bipartite Quantum Resources in Tripartite Systems

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