On the separability criterion of bipartite states with certain non-Hermitian operators

TL;DR

This paper introduces a new separability criterion for bipartite quantum states using expectation values of non-Hermitian operators, enabling detection of entanglement in higher-dimensional systems.

Contribution

It develops a novel approach to assess separability by expressing density matrix elements through non-Hermitian operator expectation values, applicable to arbitrary dimensions.

Findings

Reformulates density matrix elements via non-Hermitian operators.

Provides a criterion for bipartite state separability.

Detects entanglement in certain high-dimensional states.

Abstract

We construct a density matrix whose elements are written in terms of expectation values of non-Hermitian operators and their products for arbitrary dimensional bipartite states. We then show that any expression which involves matrix elements can be reformulated by the expectation values of these non-Hermitian operators and vice versa. We consider the condition of pure states and pure product states and rewrite them in terms of expectation values and density matrix elements respectively. We utilize expectation values of these operators to present the condition for separability of ${C}^d \otimes {C}^d$ bipartite states. With the help of our separability criterion we detect entanglement in certain classes of higher dimensional bipartite states.