Multi-party Purity Distillation and Instrument Simulation in the One-Shot Regime
Igor Bernard, Arun Padakandla
TL;DR
This work advances one-shot quantum information processing for distributed purification and measurement tasks by delivering new inner bounds for three-party purity distillation and distributed instrument simulation. It couples a one-shot PD protocol with a one-shot instrument-simulation framework that preserves post-measurement states, leveraging measurement compression, likelihood POVMs, and a COS tool to overcome nonconcentration challenges. The authors also derive asymptotic counterparts, tying the one-shot bounds to the best known asymptotic inner bounds, and extend the framework to include quantum side information at the decoder via a one-shot cq-MAC analysis. Overall, the paper provides a cohesive, technically rigorous treatment of one-shot PD and distributed instrument simulation, along with explicit rate-region characterizations that connect to established asymptotic results and extend to side-information scenarios.
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.