A characterization of entangled two-qubit states via partial-transpose-moments

TL;DR

This paper fully characterizes the region of partial-transpose moments for two-qubit states, providing new tools for detecting and understanding entanglement, and extends these methods to multiqubit states.

Contribution

It introduces a complete description of the second and third PT-moments for all two-qubit states and applies this to characterize entanglement in specific state families and multiqubit systems.

Findings

The PT-moment region for all two-qubit states is fully described.

Entanglement regions are precisely characterized using PT-moments.

The method extends to detect entanglement in multiqubit states, including GHZ and W states.

Abstract

Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial-transpose(PT)-moments of two-qubit states,and completely describe the whole region, composed of the second and third PT-moments, for all two-qubit states. Furthermore, they determine the accurate region corresponding to all entangled two-qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT-moments for the two families of Werner states and Bell-diagonal states. The relations between entanglement and the pairs of PT-moments are revealed from these typical examples. They also numerically plot the whole region of possible PT-moments for all two-qubit X-states, and find that this region is almost the same as the whole region of PT-moments for all two-qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT-moment-based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states.