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Results in Physics

Improved bounds on some entanglement criteria in bipartite quantum systems

Liang Bao Tang, Fan Wu

Published Jun 21, 2023• 6 citations
Publisher

Abstract

Entanglement detection is one of the core tasks in quantum information processing. Based on a broad class of informationally complete symmetric measurements, a series of separability criteria are proposed for different bipartite quantum systems using Cauchy–Schwarz inequality and ρ−ρA⊗ρB, respectively. In addition, by comparing and analyzing the existing entanglement criteria and detailed examples, it is not difficult to prove that our proposed criteria are more powerful and comprehensive in entanglement detection.

DOI
10.1016/j.rinp.2023.106663

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Entanglement detection is one of the core tasks in quantum information processing. Based on a broad class of informationally complete symmetric measurements, a series of separability criteria are proposed for different bipartite quantum systems using Cauchy–Schwarz inequality and ρ−ρA⊗ρB, respectively. In addition, by comparing and analyzing the existing entanglement criteria and detailed examples, it is not difficult to prove that our proposed criteria are more powerful and comprehensive in entanglement detection.
We present a unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain this general principle and show how to use it to derive not only already known entanglement criteria, but also criteria which were unknown so far. We systematically investigate its potential and limitations to detect bipartite and multipartite entanglement. Furthermore, we describe how to apply our generalized entanglement detection scheme to find the measurement directions to verify the entanglement of a given state experimentally.
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.