Partial transpose moments, principal minors and entanglement detection

Abstract

Recently, it has been shown that locally randomized measurements can be employed to get partial transpose moments of a density matrix [Elben A., et al. Phys. Rev. Lett. 125, 200501 (2020)].Consequently, two general entanglement detection methods were proposed based on partial transpose moments of a density matrix [Yu X-D., et al. Phys. Rev. Lett. 127, 060504 (2021)]. In this context, a natural question arises that how partial transpose moments are related with entanglement and with well known idea of principal minors. In this work, we analytically demonstrate that for qubit-qubit quantum systems, partial transpose moments can be expressed as simple functions of principal minors. We expect this relation to exist for every bipartite quantum systems. In addition, we have extended the idea of PT-moments for tripartite qubit systems and have shown that PT-moments can only detect the whole range of being NPT for GHZ and W states mixed with white noise.

Genuine entanglement under squeezed generalized amplitude damping channels with memory

“…[1] There is growing interest among researchers to study quantum correlations in both theory and experiments. [2][3][4][5][6] Entanglement is a precious resource and is important for several applications. However, one of the big challenges is to preserve quantum correlations in quantum states.…”

Moments based entanglement criteria and measures

“…In [39], the authors proposed a framework for designing multipartite entanglement criteria based on permutation moments. The author in [40] demonstrates that for two-qubit quantum systems the PT moments can be expressed as functions of principal minors and shows that the PT moments can detect all the negative partial transpose entanglement of GHZ and W states mixed with white noise. A separability criterion and its physical realization has been also proposed by using the moments of the realigned density matrices [41,42].…”