One-shot manipulation of coherence in dynamic quantum resource theory

TL;DR

This paper develops a one-shot theory for dynamic quantum coherence, using superchannel theory to analyze resource manipulation and establish bounds on coherence costs in quantum channels.

Contribution

It introduces a framework for dynamic quantum coherence, defining free superchannels and establishing bounds on coherence cost and distillation.

Findings

Defined dynamic coherence resources using superchannels

Established one-shot coherence cost and distillation bounds

Introduced $oldsymbol{ ext{MISC}}$ superchannels with negligible coherence generation

Abstract

A fundamental problem in quantum information is to understand the operational significance of quantum resources. Quantum resource theories (QRTs) provide a powerful theoretical framework that aids in analyzing and comprehending the operational meaning of these resources. Early resource theories primarily focused on analyzing static quantum resources. Recently, there has been growing interest in the study of dynamic quantum resources. In this paper, we utilize superchannel theory to describe the dynamic resource theory of quantum coherence. In this dynamic resource theory, we treat classical channels as free channels and consider two classes of free superchannels that preserve channel incoherence (maximally incoherent superchannels (MISC) and dephasing-covariant incoherent superchannels (DISC)) as free resources. We regard the quantum Fourier transform as the golden unit of dynamic coherence resources. We first establish the one-shot theory of dynamic coherence cost and dynamic coherence distillation, which involves converting the quantum Fourier transform into an arbitrary quantum channel using MISC and DISC. Next, we introduce a class of free superchannels known as $\delta$-MISC, which asymptotically generate negligible dynamic coherence. Finally, we provide upper and lower bounds for the one-shot catalytic dynamic coherence cost of quantum channels under the action of these $\delta$-MISC superchannels.