Enhanced realignment criterion vs linear entanglement witnesses

Sarbicki, Gniewomir; Chruściński, Dariusz; Scala, Giovanni

doi:10.1088/1751-8121/abba46

Cited by 14 publications

(13 citation statements)

References 29 publications

(43 reference statements)

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“…Hence, the enhanced realignment criterion is equivalent to the to the family of XYcriteria minimising p xy . Interestingly, in [12] we proved that this equivalence is always realized for large values of x and y, but for isotropic states in Eq. ( 5) it is enough consider x, y belonging to the hyperbola in Eq.…”

Section: Comparison With Enhanced Realignment Criterionmentioning

confidence: 68%

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Family of multipartite separability criteria based on a correlation tensor

2020

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A family of separability criteria based on correlation matrix (tensor) is provided. Interestingly, it unifies several criteria known before like e.g. CCNR or realignment criterion, de Vicente criterion and derived recently separability criterion based on SIC POVMs. It should be stressed that, unlike the well known Correlation Matrix Criterion or criterion based on Local Uncertainty Relations, the new criteria are linear in the density operator and hence one may find new classes of entanglement witnesses and positive maps. Interestingly, there is a natural generalization to multipartite scenario using multipartite correlation matrix. We illustrate the detection power of the above criteria on several well known examples of quantum states.

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Section: Comparison With Enhanced Realignment Criterionmentioning

confidence: 68%

“…Enhanced realignment criterion turns out to be the strongest effectively computable simplification of Correlation Matrix Criterion [14][15][16] (see also [17] for the unifying approach). In the recent papers [12] we showed that this criterion is equivalent to (2) for all x, y ≥ 0.…”

Section: Introductionmentioning

confidence: 96%

Family of multipartite separability criteria based on a correlation tensor

2020

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“…[13,14]. Very recently, a general approach for checking separability is taken by considering the linear correlations of specific operators in Refs [15,16], which incidentally covers both the CCNR and the ESIC criteria.…”

Section: Introductionmentioning

confidence: 99%

Operational Detection of Entanglement via Quantum Designs

2022

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From an operational point of view, we propose several new entanglement detection criteria using quantum designs. These criteria are constructed by considering the correlations defined with quantum designs. Counter-intuitively, the criteria with more settings are exactly equivalent to the corresponding ones with the minimal number of settings, namely the symmetric informationally complete positive operator-valued measures (SIC POVMs). Fundamentally, this observation highlights the potentially unique role played by SIC POVMs in quantum information processing. Experimentally, this provides the minimal number of settings that one should choose for detecting entanglement. Furthermore, we find that nonlinear criteria are not always better than linear ones for the task of entanglement detection.

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“…These were recently generalized in Refs. 13 , 14 . Another interesting class of indecomposable witnesses is constructed in terms of mutually unbiased bases 15 – 20 .…”

Section: Introductionmentioning

confidence: 99%

Entanglement witnesses from mutually unbiased measurements

Siudzińska

Chruściński

2021

Sci Rep

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A new family of positive, trace-preserving maps is introduced. It is defined using the mutually unbiased measurements, which generalize the notion of mutual unbiasedness of orthonormal bases. This family allows one to define entanglement witnesses whose indecomposability depends on the characteristics of the associated measurement operators. We provide examples of indecomposable witnesses and compare their entanglement detection properties with the realignment criterion.

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Enhanced realignment criterion vs linear entanglement witnesses

Cited by 14 publications

References 29 publications

Family of multipartite separability criteria based on a correlation tensor

Family of multipartite separability criteria based on a correlation tensor

Operational Detection of Entanglement via Quantum Designs

Entanglement witnesses from mutually unbiased measurements

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