论文标题
一般量子资源理论：蒸馏，形成和一致的资源度量
General Quantum Resource Theories: Distillation, Formation and Consistent Resource Measures
论文作者
论文摘要
量子资源理论（QRT）提供了一个统一的理论框架，用于理解固有的量子力学特性，这些质量机械性能是量子信息处理中的资源，但是由物理学动机的资源可能具有棘手的数学结构来分析，例如无限制的最大力资源能力的状态，缺乏凸度和无限的增长。我们在最小的假设下研究了一般QRT中的状态转换和资源度量，以找出可能具有如此棘手的数学结构的物理动机量子资源的普遍特性。在一般环境中，我们证明了在一声状态转换中的最大足智多谋的存在。同样，我们分析了渐近状态转换，我们发现了量子资源的催化复制，其中资源状态可通过自由操作无限复制。在QRT中，我们在不假定最大足智多谋的状态的情况下，我们制定了量子资源的蒸馏和形成的任务，并分别基于蒸馏和形成来介绍可蒸馏的资源和资源成本。此外，我们引入一致的资源度量，以量化量子资源的数量，而无需与国家conversion依的速率相矛盾，即使在具有非唯一最大机智状态的QRT中也是如此。超越了以前的工作，展示了添加资源度量的独特定理，我们证明了一致的资源度量的相应唯一性不平等；也就是说，量子状态的一致资源度量占据可蒸馏资源和国家资源成本之间的值。这些配方和结果建立了适用于数学上棘手但具有物理动机的量子资源的QRT的基础。
Quantum resource theories (QRTs) provide a unified theoretical framework for understanding inherent quantum-mechanical properties that serve as resources in quantum information processing, but resources motivated by physics may possess intractable mathematical structure to analyze, such as non-uniqueness of maximally resourceful states, lack of convexity, and infinite dimension. We investigate state conversion and resource measures in general QRTs under minimal assumptions to figure out universal properties of physically motivated quantum resources that may have such intractable mathematical structure. In the general setting, we prove the existence of maximally resourceful states in one-shot state conversion. Also analyzing asymptotic state conversion, we discover catalytic replication of quantum resources, where a resource state is infinitely replicable by free operations. In QRTs without assuming uniqueness of maximally resourceful states, we formulate the tasks of distillation and formation of quantum resources, and introduce distillable resource and resource cost based on the distillation and the formation, respectively. Furthermore, we introduce consistent resource measures that quantify the amount of quantum resources without contradicting the rate of state conversion even in QRTs with non-unique maximally resourceful states. Progressing beyond the previous work showing a uniqueness theorem for additive resource measures, we prove the corresponding uniqueness inequality for the consistent resource measures; that is, consistent resource measures of a quantum state take values between the distillable resource and the resource cost of the state. These formulations and results establish a foundation of QRTs applicable to mathematically intractable but physically motivated quantum resources in a unified way.
