Virtual quantum resource distillation: General framework and applications

TL;DR

This paper introduces a comprehensive framework for virtual quantum resource distillation, leveraging classical postprocessing to enhance quantum resource manipulation across states, channels, and processes, with broad theoretical and practical applications.

Contribution

It extends quantum resource distillation to include classical postprocessing and applies to states, channels, and higher-order processes, providing a unified, computable framework.

Findings

Framework applicable to various resource theories

Semidefinite programs for performance benchmarking

Versatile application to quantum states, channels, and dynamics

Abstract

We develop the general framework of virtual resource distillation -- an alternative distillation strategy proposed in [Phys. Rev. Lett. 132, 050203 (2024)], which extends conventional quantum resource distillation by integrating the power of classical postprocessing. The framework presented here is applicable not only to quantum states, but also dynamical quantum objects such as quantum channels and higher-order processes. We provide a general characterization and benchmarks for the performance of virtual resource distillation in the form of computable semidefinite programs as well as several operationally motivated quantities. We apply our general framework to various concrete settings of interest, including standard resource theories such as entanglement, coherence, and magic, as well as settings involving dynamical resources such as quantum memory, quantum communication, and non-Markovian dynamics. The framework of probabilistic distillation is also discussed.