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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

The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state ρ 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 E(ρN) is scalable if it can be described as a function of the variables {E(ρi1),,E(ρiq);N} for N>ij, while preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of E(ρN), which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if E(ρ2n) depends only on E(ρ), E(ρ2), and n, 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 ϱ, we determine the OSD entanglement for ϱ96 from smaller tensorings, with an accuracy of 97% 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 ρ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Ëρñ可扩展的,如果它可以被描述为变量的函数{Ëρ一世1个Ëρ一世q;ñ} 对于 ñ>一世Ĵ,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Ëρñ,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Ëρ2ñ 仅取决于 Ëρ Ëρ2ñ,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ϱ,我们确定OSD纠缠为 ϱ96 来自较小的张量,精度为 97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
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