Asymptotically consistent measures of general quantum resources: Discord, non-Markovianity, and non-Gaussianity

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.

Automated summary

Quantum resource theories offer a unified framework for quantitatively analyzing inherent quantum properties as resources for quantum information processing. This paper introduces an alternative resource measurement axiom, asymptotic consistency, which allows for quantifying resources without contradicting transformation rates. Relative entropic measures are shown to be consistent with transformation rates for various types of resources, demonstrating widely applicable quantitative analysis of quantum properties.