Virtual quantum resource distillation

TL;DR

This paper introduces virtual quantum resource distillation, a method that approximates measurement statistics rather than states, enabling purification of noisy states beyond traditional limits and with efficient cost estimation.

Contribution

It proposes a new framework for quantum resource distillation that relaxes traditional state approximation to measurement statistics, broadening the scope of resource purification.

Findings

Virtual distillation allows purification where standard methods fail.

Cost of distillation is inversely related to existing resource amount.

Efficient estimation of distillation cost via convex and semidefinite programming.

Abstract

Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted 'free' operations to convert a noisy state into one that approximates a desired pure state. Here, we propose to relax this setting by only requiring the approximation of the measurement statistics of a target pure state, which allows for additional classical postprocessing of the measurement outcomes. We show that this extended scenario, which we call virtual resource distillation, provides considerable advantages over standard notions of distillation, allowing for the purification of noisy states from which no resources can be distilled conventionally. We show that general states can be virtually distilled with a cost (measurement overhead) that is inversely proportional to the amount of existing resource, and we develop methods to efficiently estimate such cost via convex and semidefinite programming, giving several computable bounds. We consider applications to coherence, entanglement, and magic distillation, and an explicit example in quantum teleportation (distributed quantum computing). This work opens a new avenue for investigating generalized ways to manipulate quantum resources.