A Note on Normal Forms of Quantum States and Separability

TL;DR

This paper investigates the normal forms of multipartite quantum states, improving the correlation matrix separability criterion through filtering transformations and constructing entanglement witnesses using local orthogonal observables.

Contribution

It introduces an enhanced normal form for multipartite density matrices and develops improved separability criteria and entanglement witnesses based on this form.

Findings

Enhanced separability criterion via normal form

Construction of entanglement witnesses using local observables

Applicable to both bipartite and multipartite systems

Abstract

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.