Multi-party Purity Distillation and Instrument Simulation in the One-Shot Regime

TL;DR

This paper develops a one-shot multi-party purity distillation protocol that generalizes existing asymptotic bounds, enabling efficient distributed quantum state processing in the one-shot regime.

Contribution

It introduces a novel one-shot inner bound for multi-party purity distillation that extends to the asymptotic case, combining instrument simulation and local purity concentration.

Findings

Derived a new one-shot inner bound for multi-party purity distillation.

Generalized the bound to match the best known asymptotic results.

Designed a practical one-shot protocol with analyzed performance.

Abstract

We address the problem of distributed multi-party purity distillation (PD) involving three parties in the one-shot regime. By obtaining a one-shot inner bound for the distributed instrument simulation problem that naturally generalizes to the best known asymptotic inner bound, and combining with a recent one-shot single party local purity concentration protocol, we design a one-shot multi-party PD protocol, analyze performance and derive a new inner bound. The derived inner bound naturally generalizes to the best known asymptotic inner bound.