Moments based entanglement criteria and measures

TL;DR

This paper introduces new entanglement criteria based on matrix moments, providing effective, experimentally friendly methods for detecting and measuring quantum entanglement, including bounds on concurrence and measures for bipartite and tripartite states.

Contribution

It proposes novel moment-based entanglement criteria and measures that are simple to implement and more finely characterize quantum entanglement than existing methods.

Findings

Effective entanglement detection using matrix moments.

Provides experimentally measurable lower bounds of concurrence.

Characterizes bipartite and tripartite entanglement more precisely.

Abstract

Quantum entanglement plays a key role in quantum computation and quantum information processing. It is of great significance to find efficient and experimentally friend separability criteria to detect entanglement. In this paper, we firstly propose two easily used entanglement criteria based on matrix moments. The first entanglement criterion only uses the first two realignment moments of a density matrix. The second entanglement criterion is based on the moments related to the partially transposed matrix. By detailed examples we illustrate the effectiveness of these criteria in detecting entanglement. Moreover, we provide an experimentally measurable lower bound of concurrence based on these moments. Finally, we present both bipartite and genuine tripartite entanglement measures based on the moments of the reduced states. By detailed examples, we show that our entanglement measures characterize the quantum entanglement in a more fine ways than the existing measures.