Entanglement measures: state ordering vs local operations

TL;DR

This paper investigates whether local operations can alter the ordering of quantum states based on their entanglement, showing that unilocal channels can indeed change this ordering, even for maximally entangled states.

Contribution

It demonstrates that local operations can modify the entanglement-based ordering of quantum states, challenging assumptions about the invariance of maximal entanglement under local noise.

Findings

Unilocal channels can change the entanglement ordering of states.

Maximally entangled states may not remain the most entangled after local noise.

Local operations can alter the relative entanglement levels of quantum states.

Abstract

A set of all states of a bi-partite quantum system can be divided into subsets each of which contains states with the same degree of entanglement. In this paper we address a question whether local operations (without classical communication) affect the entanglement-induced state ordering. We show that arbitrary unilocal channel (i.e., a channel that acts on one sub-system of a bi-partite system only) might change the ordering for an arbitrary nontrivial measure of entanglement. A slightly weaker result holds for the maximally entangled states. In particular, the maximally entangled states might not remain the most entangled ones at the output of a unilocal noise channel.