Separability criteria based on a class of symmetric measurements

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 Siudzinska, (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 Siudzinska, 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.

Automated summary

Highly symmetric quantum measurements have significant importance in both foundational and practical aspects of quantum information theory. A recent study proposes a broad class of symmetric measurements as a generalization of mutually unbiased measurements and general symmetric informationally complete positive-operator-valued measures. The study investigates the role of these symmetric measurements in entanglement detection and presents a separability criterion for bipartite systems based on correlation matrices defined via symmetric measurements. Moreover, two efficient criteria are introduced to detect entanglement in tripartite quantum states using symmetric measurements.