Mutually unbiased measurements with arbitrary purity

Salehi, Mahdi; Akhtarshenas, Seyed Javad; Sarbishaei, Mohsen; Jaghouri, Hakimeh

doi:10.1007/s11128-021-03340-5

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…Hiesmayr et al 15 showed that inequivalent and unextendible sets of MUBs are sometimes more useful to detect entanglement, whereas Bae et al 1 found that more than MUBs are needed to identify bound entangled states. The MUMs encompassing a full range of purity were shown to detect entanglement with as little as two measurement operators 36 . Recently, it has also been proven that the witnesses constructed from MUMs belong to the class based on the CCNR criterion 40 .…”

Section: Introductionmentioning

confidence: 99%

Indecomposability of entanglement witnesses constructed from symmetric measurements

Siudzińska

2022

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We propose a family of positive maps constructed from a recently introduced class of symmetric measurements. These maps are used to define entanglement witnesses, which include other popular approaches with mutually unbiased bases and mutually unbiased measurements. A particular interest is given to indecomposable witnesses that can be used to detect entanglement of quantum states with positive partial transposition. We present several examples for different number of measurements.

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Section: Introductionmentioning

confidence: 99%

Indecomposability of entanglement witnesses constructed from symmetric measurements

Siudzińska

2022

Sci Rep

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Entanglement witnesses from mutually unbiased measurements

Siudzińska

Chruściński

2021

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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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Entropic uncertainty relations and entanglement detection from quantum designs

Zhao,

Huang,

2024

J. Phys. A: Math. Theor.

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Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved Rényi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g., squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one’s ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multi-partite entanglement with design-structured measurements.

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Mutually unbiased measurements with arbitrary purity

Cited by 3 publications

References 22 publications

Indecomposability of entanglement witnesses constructed from symmetric measurements

Indecomposability of entanglement witnesses constructed from symmetric measurements

Entanglement witnesses from mutually unbiased measurements

Entropic uncertainty relations and entanglement detection from quantum designs

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