arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1910.10285quant-ph
收藏

Characterizing scalable measures of quantum resources

Fernando Parisio

备注：
Text enlarged and improved
发表信息：
Phys. Rev. A 102, 012413 (2020)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

英文摘要：

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 ${\cal E}(ρ^{\otimes N})$ is {\it scalable} if it can be described as a function of the variables $\{{\cal E}(ρ^{\otimes i_1}),\dots,{\cal E}(ρ^{\otimes i_q}); N\}$ for $N>i_j$, while, preserving the tensor-product structure. If analyticity is assumed, recursive relations can be derived for the Maclaurin series of ${\cal E}(ρ^{\otimes N})$, which enable us to determine its possible functional forms (in terms of the mentioned variables). In particular, we find that if ${\cal E}(ρ^{\otimes 2^n})$ depends only on ${\cal E}(ρ)$, ${\cal E}(ρ^{\otimes 2})$, 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 $\varrho$, we determine the OSD entanglement for $\varrho^{\otimes 96}$ from smaller tensorings, with an accuracy of $97 \%$ and no extra computational effort. Finally, we show that superactivation of non-additivity may occur in this context.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑