Indecomposability of entanglement witnesses constructed from symmetric measurements

Siudzińska, Katarzyna

doi:10.1038/s41598-022-14920-5

Cited by 8 publications

(3 citation statements)

References 47 publications

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“…here {|k⟩} d−1 k=0 is a set of orthonormal basis in H d , which can be seen as an application of the celebrated Choi-Jamiolkowski isomorphism [24]. Recently, based on the SIC POVM and MUBs, some classes of positive maps and witness have been proposed [25,26].…”

Section: Introductionmentioning

confidence: 99%

The entanglement criteria based on equiangular tight frames

Shi

2024

J. Phys. A: Math. Theor.

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Finite tight frames play an important role in miscellaneous areas, including quantum information theory. Here we apply a class of tight frames, equiangular tight frames, to address the problem of detecting the entanglement of bipartite states. Here we derive some entanglement criteria based on positive operator-valued measurements built from equiangular tight frames. We also present a class of entanglement witnesses based on the equiangular tight frames. At last, we generalize the entanglement criterion for bipartite systems to multipartite systems.

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Section: Introductionmentioning

confidence: 99%

The entanglement criteria based on equiangular tight frames

Shi

2024

J. Phys. A: Math. Theor.

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“…In 2018, Chruscinski et al showed a method to construct entanglement witnesses from mutually unbiased bases (MUB) [19]. Whereafter, the authors in [20][21][22] generalized the method to build entanglement witnesses with other classes of positive operator-valued measurements (POVM). Quantifying the entanglement of a bipartite state is the other important problem in entanglement theory [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Families of Schmidt-number witnesses for high dimensional quantum states

Shi

2024

Commun. Theor. Phys.

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Higher dimensional entangled states demonstrate significant advantages in quantum information processing tasks. The Schmidt number is a quantity of the entanglement dimension of a bipartite state. Here we build families of k-positive maps from the symmetric information complete positive operator-valued measurements and mutually unbiased bases, and we also present the Schmidt number witnesses, correspondingly. At last, based on the witnesses obtained from mutually unbiased bases, we show the distance between a bipartite state and the set of states with a Schmidt number less than k.

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“…Recently, Siudzińska introduced a broad class of symmetric measurements [46], which includes the MUMs and GSIC-POVMs as special cases. Moreover, possible applications of these symmetric measurements are further discussed in [46][47][48], such as the entropic uncertainty relations and entanglement detection.…”

Section: Introductionmentioning

confidence: 99%

Separability criteria based on a class of symmetric measurements

Lai¹,

Luo

2023

Commun. Theor. Phys.

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Highly symmetric quantum measurements, such as mutually unbiased measurements (MUMs) and general symmetric informationally complete positive-operator-valued measures (GSIC-POVMs), play an important role both in foundations and practical aspects of quantum information theory. Recently, a broad class of symmetric measurements was introduced [ K. Siudzin′ska, Phys. Rev. A 105, 042209 (2022)], which can be viewed as a common generalization of MUMs and GSIC-POVMs. In this work, the role of these symmetric measurements in entanglement detection is studied. More specifically, based on the correlation matrices defined via (informationally complete) symmetric measurements, a separability criterion for arbitrary dimensional bipartite systems is proposed. It is shown that the criterion is stronger than the method provided by Siudzin′ska, meanwhile, it can unify several popular separability criteria based on MUMs or GSIC-POVMs. Furthermore, using these (informationally complete) symmetric measurements, two efficient criteria are presented to detect the entanglement of tripartite quantum states. The detection power and advantages of these criteria are illustrated through several examples.

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Indecomposability of entanglement witnesses constructed from symmetric measurements

Cited by 8 publications

References 47 publications

The entanglement criteria based on equiangular tight frames

The entanglement criteria based on equiangular tight frames

Families of Schmidt-number witnesses for high dimensional quantum states

Separability criteria based on a class of symmetric measurements

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