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Characterizing scalable measures of quantum resources
Physical Review A ( IF 2.9 ) Pub Date : 2020-07-10 , DOI: 10.1103/physreva.102.012413 Fernando Parisio
Physical Review A ( IF 2.9 ) Pub Date : 2020-07-10 , DOI: 10.1103/physreva.102.012413 Fernando Parisio
The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we propose a way to circumvent the direct evaluation of such quantities, provided that the employed measures satisfy a self-similarity property. We say that a quantity is scalable if it can be described as a function of the variables for , while preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of , which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if depends only on , and , then it is completely determined by Fibonacci polynomials, to leading order. We show that the one-shot distillable (OSD) entanglement is well described as a scalable measure for several families of states. For a particular two-qutrit state , we determine the OSD entanglement for from smaller tensorings, with an accuracy of and no extra computational effort. Finally, we show that superactivation of nonadditivity may occur in this context.
中文翻译:
表征量子资源的可扩展度量
数量(如纠缠和连贯性)如何取决于给定状态的副本数的问题 已解决。这是一个难题,通常涉及对大尺寸希尔伯特空间的优化。在这里,我们提出了一种方法来规避对此类数量的直接评估,只要所采用的措施满足自相似性即可。我们说一个数量是可扩展的,如果它可以被描述为变量的函数 对于 ,同时保留张量积结构。如果假设分析性,则可以推导麦克劳林级数的递归关系,这使我们能够确定其可能的功能形式(就上述变量而言)。特别是,我们发现如果 仅取决于 和 ,则完全由Fibonacci多项式确定,直至领先。我们表明,一次蒸馏可蒸馏(OSD)纠缠被很好地描述为几个状态族的可扩展度量。对于特定的二态状态,我们确定OSD纠缠为 来自较小的张量,精度为 无需额外的计算工作。最后,我们证明了在这种情况下可能发生非加性的超活化。
更新日期:2020-07-10
中文翻译:
表征量子资源的可扩展度量
数量(如纠缠和连贯性)如何取决于给定状态的副本数的问题 已解决。这是一个难题,通常涉及对大尺寸希尔伯特空间的优化。在这里,我们提出了一种方法来规避对此类数量的直接评估,只要所采用的措施满足自相似性即可。我们说一个数量是可扩展的,如果它可以被描述为变量的函数 对于 ,同时保留张量积结构。如果假设分析性,则可以推导麦克劳林级数的递归关系,这使我们能够确定其可能的功能形式(就上述变量而言)。特别是,我们发现如果 仅取决于 和 ,则完全由Fibonacci多项式确定,直至领先。我们表明,一次蒸馏可蒸馏(OSD)纠缠被很好地描述为几个状态族的可扩展度量。对于特定的二态状态,我们确定OSD纠缠为 来自较小的张量,精度为 无需额外的计算工作。最后,我们证明了在这种情况下可能发生非加性的超活化。