Entanglement criterion via general symmetric informationally complete measurements

Lai, Le-Min; Li, Tao; Fei, Shao-Ming

doi:10.1007/s11128-018-2084-6

Cited by 10 publications

(13 citation statements)

References 52 publications

(97 reference statements)

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“…Interestingly, if we choose MUMs or GSIC-POVMs as local measurements for the two subsystems, respectively, then the separability criteria determined by equations (11), ( 13), ( 15) and ( 16) can recover the ones in [36][37][38][39][40][41][42], as summarized in table 2.  by…”

Section: Letmentioning

confidence: 99%

“…Moreover, unlike the MUBs and SIC-POVMs, the complete set of MUMs and GSIC-POVMs can be constructed explicitly in all finite dimensions. These measurements are widely applied to the detection of entanglement, and thus a series of efficient separability criteria have been proposed both for bipartite and multipartite systems to date [36][37][38][39][40][41][42][43][44][45]. It has been shown that the existing criteria based on MUMs and GSIC-POVMs are very powerful in detecting the entanglement of bipartite quantum states, however, how to construct efficient criteria for multipartite quantum states is in general a hard issue.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Separability criteria based on a class of symmetric measurements

Lai¹,

Luo

2023

Commun. Theor. Phys.

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“…We discuss in this section testers coming from spherical 2-designs; an important special case corresponds to the entanglement criterion based on SIC POVMs introduced in [SAZG18, Section IV] (see also [LLFW18]). Given a spherical 2-design {|x k } d 2 k=1 of C d with d 2 elements (see equation ( 14) below for the definition), the set…”

Section: Important Examples Of Testersmentioning

confidence: 99%

Multipartite entanglement detection via projective tensor norms

Jivulescu¹,

Lancien²,

Nechita³

2020

Preprint

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We introduce and study a class of entanglement criteria based on the idea of applying local contractions to an input multipartite state, and then computing the projective tensor norm of the output. More precisely, we apply to a mixed quantum state a tensor product of contractions from the Schatten class S1 to the Euclidean space 2, which we call entanglement testers. We analyze the performance of this type of criteria on bipartite and multipartite systems, for general pure and mixed quantum states, as well as on some important classes of symmetric quantum states. We also show that previously studied entanglement criteria, such as the realignment and the SIC POVM criteria, can be viewed inside this framework. This allows us to answer in the positive two conjectures of Shang, Asadian, Zhu, and Gühne by deriving systematic relations between the performance of these two criteria.

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“…Uncertainty relations of GSIC POVMs are studied in different contexts such as the entropic uncertainty relation [15], the uncertainty and complementarity relation using generalized Wigner-Yanase-Dyson skew information [16], and the improved state-dependent entropic uncertainty relation [17]. Entanglement detection using the index of coincidence for GSIC POVMs as well as its experimental implementation has also been studied in [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Construction of general symmetric-informationally-complete–positive-operator-valued measures by using a complete orthogonal basis

Yoshida

Kimura

2022

Phys. Rev. A

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A general symmetric informationally complete (GSIC)-positive operator valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC-POVMs with a fixed average purity. In this paper, we provide a general construction of a GSIC-POVM by means of a complete orthogonal basis (COB), also interpreted as a normal quasiprobability representation. A spectral property of a COB is shown to play a key role in the construction of SIC-POVMs and also for the bound of the mean-square error of the state tomography. In particular, a necessary and sufficient condition to construct a SIC POVM for any d is constructively given by the power of traces of a COB. We give three simple constructions of COBs from which one can systematically obtain GSIC POVMs.

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Entanglement criterion via general symmetric informationally complete measurements

Cited by 10 publications

References 52 publications

Separability criteria based on a class of symmetric measurements

Separability criteria based on a class of symmetric measurements

Multipartite entanglement detection via projective tensor norms

Construction of general symmetric-informationally-complete–positive-operator-valued measures by using a complete orthogonal basis

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