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.

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一般量子资源的渐近一致度量：Discord、非马尔可夫性和非高斯性

量子资源理论提供了一个统一的框架来定量分析作为量子信息处理资源的内在量子特性。为了研究量化资源的最佳方法，已经通过公理化方法广泛研究了资源量化的可取公理。然而，由于转换中的近似，通过具有此类所需公理的资源度量进行资源量化的常规方法可能与资源丰富的量子状态之间的渐近转换率相矛盾。在本文中，我们建立了一个替代公理，资源度量的渐近一致性，并且我们研究了渐近一致的资源度量，在不与渐近资源转换率相矛盾的情况下量化资源。我们证明相对熵测度与大类资源的速率一致，即所有凸有限维资源，例如纠缠、相干和魔法，甚至一些非凸或无限维资源，例如量子不和谐，非马尔可夫性和非高斯性。这些结果表明，一致的资源度量广泛适用于各种固有量子力学特性的定量分析。