Quantifying Dynamical Total Coherence in a Resource Non-increasing Framework

TL;DR

This paper introduces methods to quantify dynamical quantum resources within a resource non-increasing framework, demonstrating their application to total coherence and providing both analytical and numerical tools for evaluation.

Contribution

It proposes two approaches—distance measures and maximal increasing static resource—for quantifying dynamical resources, with applications to total coherence and specific quantum channels.

Findings

Distance measures have operational meaning and are computable via SDP.

MISR-based measures can yield analytical solutions.

Application to qubit amplitude damping channel demonstrates effectiveness.

Abstract

We quantify the dynamical quantum resource in the resource non-increasing (RNI) framework, namely, the free dynamical resource is defined by the channels that cannot increase the static resourcefulness of any input state. We present two kinds of approaches to quantifying the dynamical resource, the distance measures and the maximal increasing static resource (MISR). As a demonstration, we quantify the dynamical total coherence with our presented measures. It is shown that the distance based measures have good operational interpretation through quantum processing tasks and can be numerically calculated by semidefinite programming (SDP) and the measures based on MISR could lead to the analytical solution. As an application, we consider the dynamical total coherence of the qubit amplitude damping channel. Both the analytical measure based on the static l2 norm and the numerical illustrations based on the SDP are given.