Multipartite Entanglement Evolution Under Separable Operations

TL;DR

This paper investigates how multipartite entanglement diminishes under separable operations, revealing measure and state independence in the average entanglement decay, and introduces the concept of the channel's disentangling power.

Contribution

It extends previous bipartite and multipartite entanglement decay results to general separable operations, showing measure and state invariance in entanglement decay ratios.

Findings

Average entanglement decay ratio is measure and state independent.

Separable operations' disentangling power exhibits similar invariance.

Extends bipartite and multipartite entanglement decay results to broader classes of operations.

Abstract

We study how multi-partite entanglement evolves under the paradigm of separable operations, which include the local operations and classical communication (LOCC) as a special case. We prove that the average "decay" of entanglement induced by a separable operation is measure independent (among SL-invariant ones) and state independent: the ratio between the average output entanglement and the initial entanglement is solely a function of the separable operation, regardless of the input state and of the SL-invariant entanglement measure being used. We discuss the "disentangling power" of a quantum channel and show that it exhibits a similar state invariance as the average entanglement decay ratio. Our Rapid Communication significantly extends the bipartite results of Ref. [1-3] as well as the multi-partite one of Ref. [4], all of the previous work being restricted to one-sided or particular noise models.