Quantum Dynamical Resource Theory under Resource Non-increasing Framework

TL;DR

This paper introduces a resource non-increasing framework for quantum dynamical resource theory, proposing quantification methods for dynamical coherence and demonstrating their operational significance through quantum discrimination tasks.

Contribution

It defines the RNI framework for dynamical resources, proposes new quantifiers, and connects them to operational tasks, advancing understanding of quantum dynamical coherence.

Findings

Quantified dynamical coherence with and without post-selection.

Identified free operations in dynamical coherence resource theory.

Provided analytic calculations for amplitude damping channel.

Abstract

We defne the resource non-increasing (RNI) framework to study the dynamical resource theory. With such a defnition, we propose several potential quantifcation candidates under various free operation sets. For explicit demonstrations, we quantify the quantum dynamical coherence in the scenarios with and without post-selective measurements. Correspondingly, we show that maximally incoherent operations (MIO) and incoherent operations (IO) in the static coherence resource theory are free in the sense of dynamical coherence. We also provide operational meanings for the measures by the quantum discrimination tasks. Moreover, for the dynamical total coherence, we also present convenient measures and give the analytic calculation for the amplitude damping channel.