一般量子资源的渐近一致度量：量子失谐、非马尔可夫性与非高斯性
Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
AI总结：
本文提出资源度量的渐近一致性公理，证明相对熵度量对包括量子失谐、非马尔可夫性和非高斯性在内的广泛资源类均与渐近变换速率一致，为一般量子资源提供了不矛盾的量化方法。
摘要：
量子资源理论提供了一个统一框架，用于定量分析作为量子信息处理资源的固有量子性质。为了研究量化资源的最佳方式，人们通过公理化方法广泛研究了资源量化所应满足的理想公理。然而，用满足这些理想公理的资源度量进行资源量化的传统方式，可能由于变换中的近似而与资源态之间渐近变换的速率相矛盾。在本文中，我们建立了一个替代公理，即资源度量的渐近一致性，并研究了渐近一致的资源度量，这类度量在量化资源时不会与渐近资源变换的速率相矛盾。我们证明，相对熵度量与一大类资源的速率一致，即所有凸的有限维资源，例如纠缠、相干性和魔态，甚至包括一些非凸或无限维资源，如量子失谐、非马尔可夫性和非高斯性。这些结果表明，一致的资源度量可广泛应用于对各种固有量子力学性质的定量分析。
英文摘要：
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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