Distributed Compression and Multiparty Squashed Entanglement

TL;DR

This paper investigates a multiparty quantum communication protocol for distributed state transfer, establishing bounds on achievable rates using multiparty squashed entanglement, extending the quantum Slepian-Wolf protocol.

Contribution

It introduces bounds on the rate region for multiparty quantum compression and links these bounds to the multiparty squashed entanglement measure.

Findings

Inner bounds on achievable rates derived from protocol vertices and facet inequalities.

Outer bounds established based on multiparty squashed entanglement.

Protocol generalizes the fully quantum Slepian-Wolf to multiple parties.

Abstract

We study a protocol in which many parties use quantum communication to transfer a shared state to a receiver without communicating with each other. This protocol is a multiparty version of the fully quantum Slepian-Wolf protocol for two senders and arises through the repeated application of the two-sender protocol. We describe bounds on the achievable rate region for the distributed compression problem. The inner bound arises by expressing the achievable rate region for our protocol in terms of its vertices and extreme rays and, equivalently, in terms of facet inequalities. We also prove an outer bound on all possible rates for distributed compression based on the multiparty squashed entanglement, a measure of multiparty entanglement.