Relative Quantum Resource Theory and Operational Applications in Subchannel Discrimination

TL;DR

This paper extends quantum resource theory by defining relative superiority of resources and introduces measures that quantify maximal advantage or minimal disadvantage in subchannel discrimination tasks, broadening operational interpretations.

Contribution

It proposes a relative framework for quantum resources, including new measures for advantage and deficiency, applicable to coherence and entanglement in operational tasks.

Findings

The generalized robustness measure quantifies relative advantage in subchannel discrimination.

The geometric measure accurately quantifies minimal disadvantage in resource comparison.

The framework applies to quantum coherence and entanglement, expanding resource theory scope.

Abstract

A central problem in quantum resource theory is to give operational meaning to quantum resources that can provide clear advantages in certain physical tasks compared to the convex set of resource-free states. We propose to extend this basic principle by defining the relative superiority of resources over a specific convex set of resource states, also provide a relative advantage in physical tasks based on this extended principle. This allows the generalized robustness measure to quantify the relative maximal advantage due to a given resource state over a specific convex set of resource states in the subchannel discrimination, thereby showing that the operational interpretation of resource measures also holds in a relative perspective. In addition, we offer a new framework for defining the deficiency of a given state in physical tasks compared to the set of maximum resource states. The geometric measure we provide satisfies the conditions of the framework for quantum coherence and entanglement, and it accurately quantifies the minimal disadvantage due to a given state compared to maximumresourcestates inthe subchannel discrimination in certain situations. These two extensions and new interpretations expand the scope of quantum resource theories and provide a more comprehensive operational interpretation.