One-shot purity distillation with local noisy operations and one-way classical communication

TL;DR

This paper establishes one-shot bounds for local purity distillation in quantum systems, considering noisy operations and classical communication, and connects these bounds to known asymptotic rates.

Contribution

It provides the first one-shot achievable bounds for local purity distillation with noisy operations and classical communication, extending asymptotic results to the one-shot regime.

Findings

Derived one-shot achievable bounds using mutual information-like quantities.

Bounded the rates considering local ancillas and noisy operations.

Connected one-shot bounds to asymptotic rates in the limit.

Abstract

Local pure states represent a fundamental resource in quantum information theory. In this work we obtain one-shot achievable bounds on the rates for local purity distillation, in the single-party and in the two-party cases. In both situations, local noisy operations are freely available, while in the two-party case also one-way classical communication can be used. In addition, in both situations local pure ancillas can be borrowed, as long as they are discounted from the final net rate of distillation. The one-shot rates that we obtain, written in terms of mutual information-like quantities, are shown to recover in the limit the asymptotic i.i.d. rates of Devetak [PRA, 2005], up to first order analysis.