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Improved separability criteria via some classes of measurements

Shen, S., Li, M., Li-Jost, X., Fei, S.

Published Jan 1, 2018• 13 citations
OpenAlex

Abstract

The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria for bipartite quantum states, which, by theoretical analysis, are stronger than the related existing criteria via these measurements. Two detailed examples are supplemented to show the efficiency of the presented separability criteria.

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The entanglement detection via local measurements can be experimentally implemented. Based on mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures, we present separability criteria for bipartite quantum states, which, by theoretical analysis, are stronger than the related existing criteria via these measurements. Two detailed examples are supplemented to show the efficiency of the presented separability criteria.
Based on the mutually unbiased bases, the mutually unbiased measurements and the general symmetric informationally complete positive-operator-valued measures, we propose three separability criteria for ddd-dimensional bipartite quantum systems, which are more powerful than the corresponding ones introduced previously [C. Spengler, M. Huber, S. Brierley, T. Adaktylos, and B. C. Hiesmayr, Phys. Rev. A 86, 022311 (2012); B. Chen, T. Ma, and S. M. Fei, Phys. Rev. A 89, 064302 (2014); and B. Chen, T. Li, and S. M. Fei, arXiv:1406.7820v1 [quant-ph] (2014)]. Some states such as Werner states and Bell-diagonal states are used to further illustrate the efficiency of the presented criteria.
Abstract 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 in both foundational and practical aspects of quantum information theory. Recently, a broad class of symmetric measurements were introduced [K Siudzińska, (2022) Phys. Rev. A 105, 042209], 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 Siudzińska, 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.
Abstract Quantum measurements based on mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete positive operator valued measurements, which are commonly used in quantum information and quantum computation. In this paper, by a broad class of informationally complete symmetric measurements and correlation matrices, some separability criteria are proposed for different quantum systems that are more robust and comprehensive than the corresponding criteria previously introduced L M Lai, T Li, S M Fei, and Z X Wang, (2018 Quantum Inf. Process., 17, 314); J W Shang, A Asadian, and H J Zhu, (2018 Phys. Rev. A 98, 022309). Furthermore, we extend the separability criteria of tripartite quantum systems to many-body systems. The proposed entanglement criteria may further enrich the relationship between quantum entanglement and measurement.
Mutually unbiased measurements (MUMs) are generalized from the concept of mutually unbiased bases (MUBs) and include the complete set of MUBs as a special case, but they are superior to MUBs as they do not need to be rank one projectors. We investigate entanglement detection using sets of MUMs and derive separability criteria for multipartite qudit systems, arbitrary high-dimensional bipartite systems of a d1-dimensional subsystem and a d2-dimensional subsystem, and multipartite systems of multi-level subsystems. These criteria are of the advantages of more effective and wider application range than previous criteria. They provide experimental implementation in detecting entanglement of unknown quantum states.