Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity

TL;DR

This paper introduces an alternative axiom for quantum resource measures, called asymptotic consistency, ensuring that resource quantification aligns with asymptotic transformation rates across diverse quantum properties.

Contribution

It establishes that relative entropic measures are asymptotically consistent for a wide range of quantum resources, including convex, nonconvex, and infinite-dimensional properties.

Findings

Relative entropic measures are consistent for convex finite-dimensional resources.

They also apply to some nonconvex and infinite-dimensional resources.

The framework unifies resource quantification across various quantum properties.

Abstract

Quantum resource theories provide a unified framework to quantitatively analyze inherent quantum properties as resources for quantum information processing. So as to investigate the best way for quantifying resources, desirable axioms for resource quantification have been extensively studied through axiomatic approaches. However, a conventional way of resource quantification by resource measures with such desired axioms may contradict rates of asymptotic transformation between resourceful quantum states due to an approximation in the transformation. In this paper, we establish an alternative axiom, asymptotic consistency of resource measures, and we investigate asymptotically consistent resource measures, which quantify resources without contradicting the rates of the asymptotic resource transformation. We prove that relative entropic measures are consistent with the rates for a broad class of resources, i.e., all convex finite-dimensional resources, e.g., entanglement, coherence, and magic, and even some nonconvex or infinite-dimensional resources such as quantum discord, non-Markovianity, and non-Gaussianity. These results show that consistent resource measures are widely applicable to the quantitative analysis of various inherent quantum-mechanical properties.