We study the quantum separability problem by using general symmetric informationally complete measurements and present a separability criterion for arbitrary dimensional bipartite systems. We show by detailed examples that our criterion is more powerful than the existing ones in entanglement detection.
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.
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.