Quantum coherences, K-way negativities and multipartite entanglement

TL;DR

This paper introduces a new framework for characterizing multipartite quantum states using K-way negativities, focusing on K-way coherences to better understand entanglement structure.

Contribution

It proposes a novel approach defining K-way partial transposes and negativities, providing a detailed measure of K-way coherences in N-partite quantum states.

Findings

Defined K-way partial transpose focusing on coherences

Derived fraction of K-way negativity contributing to total negativity

Identified entanglement measures as partial K-way negativities

Abstract

A characterization of N-partite states, based on K-way (K = 2 to N) negativities, is proposed. The K-way partial transpose with respect to a subsystem is defined so as to shift the focus to K-way coherences instead of K subsystems of the composite system. For an N-partite system the fraction of K-way negativity, contributing to global negativity, is obtained. The entanglement measures for a given state ${\rho}$ are identified as the partial K-way negativities of the corresponding canonical state.