Detecting entanglement of states by entries of their density matrices

TL;DR

This paper introduces a universal entanglement witness for bipartite pure states of rank-4 and a method to detect entanglement solely through density matrix entries in a specific basis.

Contribution

It presents a universal entanglement witness for rank-4 pure states and a novel approach to detect entanglement using only density matrix entries.

Findings

Universal entanglement witness for rank-4 pure states

Method to detect entanglement via density matrix entries

Construction of finite rank entanglement witnesses

Abstract

For any bipartite systems, a universal entanglement witness of rank-4 for pure states is obtained and a class of finite rank entanglement witnesses is constructed. In addition, a method of detecting entanglement of a state only by entries of its density matrix with respect to some product basis is obtained.