Uncertainty inequalities as entanglement criteria for negative partial-transpose states

TL;DR

This paper introduces a novel method using uncertainty relations as criteria to identify entanglement in quantum states, especially negative partial-transpose states, with practical experimental implications.

Contribution

It develops a systematic approach to derive separability conditions for negative partial-transpose states using uncertainty inequalities, applicable to continuous-variable systems.

Findings

Derived entanglement criteria from Schrödinger-Robertson inequalities

Provided experimentally accessible conditions for negative partial-transpose states

Established a link between uncertainty violations and quantum entanglement

Abstract

In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudo-spin observables for an arbitrary non-positive Hermitian matrix whose uncertainty relation is violated. This method enables us to systematically derive separability conditions for all negative partial-transpose states in experimentally accessible forms. In particular, generalized entanglement criteria are derived from the Schrodinger-Robertson inequalities for bipartite continuous-variable states.