Uncertainty relation and inseparability criterion

TL;DR

This paper explores an entanglement criterion based on uncertainty relations and the PPT criterion, providing a stronger separability test for bipartite quantum systems, especially effective for Werner states.

Contribution

It introduces a new separability inequality derived from the Schrödinger-Robertson uncertainty relation that outperforms previous entanglement witnesses.

Findings

The inequality distinguishes separable and entangled states effectively.

It is stronger than existing bi-linear entanglement witnesses.

It successfully identifies Werner states as separable or entangled.

Abstract

We investigate the Peres-Horodecki positive partial transpose (PPT) criterion in the context of conserved quantities and derive a condition of in- separability for a composite bipartite system depending only on the dimen- sions of its subsystems, which leads to a bi-linear entanglement witness for the two qubit system. A separability inequality using generalized Schrodinger- Robertson uncertainty relation taking suitable operators, has been derived, which proves to be stronger than the bi-linear entanglement witness operator. In the case of mixed density matrices, it identically distinguishes the separable and non separable Werner states.