Entanglement polygon inequality in qubit systems

Qian, Xiao–Feng; Alonso, Miguel A.; Eberly, J. H.

doi:10.1088/1367-2630/aac3be

Cited by 33 publications

(35 citation statements)

References 31 publications

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“…Those three bipartite entanglements were found not completely independent by Qian et al [27]. In their work, the entanglement polygon inequality states that one entanglement cannot exceed the sum of the other two,…”

Section: Introductionmentioning

confidence: 88%

“…Proof. We consider two types of bipartite entanglement, the squared concurrence C 2 and the normalized Schmidt weight Y [27]. Their relation is given by…”

Section: Appendix: Proof Of Theoremmentioning

confidence: 99%

“…An obvious geometric interpretation [27] for these inequalities is that the three squared (or not) one-to-other concurrences can represent the lengths of the three edges of a triangle. When referred to the squared formula (3), we will call it the concurrence triangle.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Triangle Governs Genuine Tripartite Entanglement

Xie,

Eberly

2021

Preprint

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A previously overlooked constraint for the distribution of entanglement in three-qubit systems is exploited for the first time and used to reveal a new genuine tripartite entanglement measure. It is interpreted as the area of a so-called concurrence triangle and is compared with other existing measures. The new measure is found superior to previous attempts for different reasons. A specific example is illustrated to show that two tripartite entanglement measures can be inequivalent due to the high dimensionality of the Hilbert space.

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Section: Introductionmentioning

confidence: 88%

“…Proof. We consider two types of bipartite entanglement, the squared concurrence C 2 and the normalized Schmidt weight Y [27]. Their relation is given by…”

Section: Appendix: Proof Of Theoremmentioning

confidence: 99%

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A Triangle Governs Genuine Tripartite Entanglement

Xie,

Eberly

2021

Preprint

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“…[28]. The triangle concurrence for three-qubit state is constitute from the following triangle relation [28,39,40]:…”

Section: Genuine Entanglement Measurementioning

confidence: 99%

Genuine multipartite entanglement measure

Guo,

Jia,

et al. 2021

Preprint

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Quantifying genuine entanglement is a crucial task in quantum information theory. In this work, we give an approach of constituting genuine m-partite entanglement measure from any bipartite entanglement and any k-partite entanglement measure, 3 ≤ k < m. In addition, as a complement to the three-qubit concurrence triangle proposed in [Phys. Rev. Lett., 127, 040403], we show that the triangle relation is also valid for any other entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri-and four-partite cases.

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“…The traditional monogamy inequality (2) provides a lower bound for "one-to-group" entanglement, such "one-to-group" entanglements are also named quantum marginal entanglements [32]. There is another kind of entanglement distribution relation giving an upper bound for quantum marginal entanglements as the following polygon inequality [33]:…”

Section: Introductionmentioning

confidence: 99%

A new entanglement measure based dual entropy

Yang¹,

Yang²,

Zhao³

et al. 2022

Preprint

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Quantum entropy is an important measure for describing the uncertainty of a quantum state, more uncertainty in subsystems implies stronger quantum entanglement between subsystems. Our goal in this work is to quantify bipartite entanglement using both von Neumann entropy and its complementary dual. We first propose a type of dual entropy from Shannon entropy. We define S t -entropy entanglement based on von Neumann entropy and its complementary dual. This implies an analytic formula for two-qubit systems. We show that the monogamy properties of the S t -entropy entanglement and the entanglement of formation are inequivalent for high-dimensional systems. We finally prove a new type of entanglement polygon inequality in terms of S t -entropy entanglement for quantum entangled networks. These results show new features of multipartite entanglement in quantum information processing.

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Entanglement polygon inequality in qubit systems

Cited by 33 publications

References 31 publications

A Triangle Governs Genuine Tripartite Entanglement

A Triangle Governs Genuine Tripartite Entanglement

Genuine multipartite entanglement measure

A new entanglement measure based dual entropy

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