One-shot Multiparty State Merging

TL;DR

This paper introduces a novel one-shot multiparty state merging protocol that efficiently interpolates between rate points without time-sharing, compares it to naive strategies, and extends to split-transfer with applications in assisted entanglement distillation.

Contribution

It presents a new one-shot multiparty state merging protocol that avoids time-sharing and analyzes its entanglement costs using min- and max-entropies, also extending to split-transfer scenarios.

Findings

Protocol allows interpolation between rate region corners without time-sharing.

Comparison shows the protocol's efficiency over naive single-party merging strategies.

Application to assisted entanglement distillation demonstrates practical utility.

Abstract

We present a protocol for performing state merging when multiple parties share a single copy of a mixed state, and analyze the entanglement cost in terms of min- and max-entropies. Our protocol allows for interpolation between corner points of the rate region without the need for time-sharing, a primitive which is not available in the one-shot setting. We also compare our protocol to the more naive strategy of repeatedly applying a single-party merging protocol one party at a time, by performing a detailed analysis of the rates required to merge variants of the embezzling states. Finally, we analyze a variation of multiparty merging, which we call split-transfer, by considering two receivers and many additional helpers sharing a mixed state. We give a protocol for performing a split-transfer and apply it to the problem of assisted entanglement distillation.