Strong entanglement criteria for mixed states, based on uncertainty relations

TL;DR

This paper introduces a new entanglement criterion for mixed states based on quantum uncertainty and skew information, which outperforms existing criteria in detecting entanglement.

Contribution

It presents a novel entanglement criterion for mixed states that isolates quantum uncertainty and surpasses previous methods in identifying entanglement.

Findings

Effective in detecting entanglement in Werner states

Stronger than existing criteria for mixed states

Reduces to Schrödinger-Robertson inequality for pure states

Abstract

We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner-Yanase skew information. The variances in this uncertainty relation does not involve any classical mixing uncertainty, and thus turns out to be purely of quantum mechanical nature. We show that any mixed entangled state can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including Werner states and it turns out to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The proposed criterion reduces to the Schrodinger-Robertson inequality for pure states.