Multipartite entanglement theory with entanglement-nonincreasing operations

TL;DR

This paper extends the resource theory of multipartite entanglement to include entanglement-nonincreasing operations, revealing that transformation rates are governed by bipartite entanglement measures and enabling reversible synthesis of tripartite states from bipartite entanglement.

Contribution

It introduces a new framework allowing small entanglement increases, simplifying multipartite entanglement transformations to bipartite entanglement measures.

Findings

Transformation rates are dictated by bipartite entanglement entropies.

Tripartite entanglement can be reduced to bipartite analogs.

Pure tripartite states can be reversibly synthesized from bipartite singlets.

Abstract

A key problem in quantum information science is to determine optimal protocols for the interconversion of entangled states shared between remote parties. While for two parties a large number of results in this direction is available, the multipartite setting still remains a major challenge. In this article, this problem is addressed by extending the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. Specifically, we consider transformations capable of introducing a small, controllable increase of entanglement of a state, with the requirement that the increase can be made arbitrarily small. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states. Remarkably, this approach allows the reduction of tripartite entanglement to its bipartite analog, indicating that every pure tripartite state can be reversibly synthesized from a suitable number of singlets distributed between pairs of parties.