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arXiv 1608.04818quant-ph
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优控格点上两体纯态纠缠的近似变换

Approximate transformations of bipartite pure-state entanglement from the majorization lattice

G. M. Bosyk, G. Sergioli, H. Freytes, F. Holik, G. Bellomo

备注：
Revised manuscript close to the accepted version in Physica A (10 pages, 1 figure)
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摘要：

利用\textit{local operations and classical communication}（LOCC）研究了\textit{initial}纯纠缠量子态$|ψ\rangle$到\textit{target}纯纠缠量子态$|ϕ\rangle$的确定性变换问题.一个著名的结果尼尔森[物理。\textbf{83}，436（1999）]给出了使这种纠缠变换过程成为可能的充分必要条件。实际上，当且仅当优序关系$ψ\prec ϕ$成立时，才能实现该过程，其中$ψ$和$ϕ$分别是通过对初始状态和目标状态的施密特系数取平方而获得的概率向量。一般来说，这个条件是不满足的。然而，我们可以寻找\textit{approximate}纠缠变换。Vidal \textit{et. al} [Phys.Rev.A \textbf{62}，012304（2000）]提出了使用LOCC的确定性变换，以便获得在它们之间的最大保真度方面最接近于$|ϕ\rangle$的目标状态$|χ^\mathrm{opt}\rangle$。在这里，我们展示了一种策略来处理基于\textit{majorization lattice}的属性的近似纠缠变换。更确切地说，我们提出了近似的目标状态的施密特系数给出的上确界之间的$ψ$和$ϕ$。我们的建议的灵感来自观察，保真度不尊重一般的优势关系。值得注意的是，我们发现，对于一些特别有趣的情况，如两个量子比特的纯态或纠缠浓度协议，这两个建议是一致的。

英文摘要：

We study the problem of deterministic transformations of an \textit{initial} pure entangled quantum state, $|ψ\rangle$, into a \textit{target} pure entangled quantum state, $|ϕ\rangle$, by using \textit{local operations and classical communication} (LOCC). A celebrated result of Nielsen [Phys. Rev. Lett. \textbf{83}, 436 (1999)] gives the necessary and sufficient condition that makes this entanglement transformation process possible. Indeed, this process can be achieved if and only if the majorization relation $ψ\prec ϕ$ holds, where $ψ$ and $ϕ$ are probability vectors obtained by taking the squares of the Schmidt coefficients of the initial and target states, respectively. In general, this condition is not fulfilled. However, one can look for an \textit{approximate} entanglement transformation. Vidal \textit{et. al} [Phys. Rev. A \textbf{62}, 012304 (2000)] have proposed a deterministic transformation using LOCC in order to obtain a target state $|χ^\mathrm{opt}\rangle$ most approximate to $|ϕ\rangle$ in terms of maximal fidelity between them. Here, we show a strategy to deal with approximate entanglement transformations based on the properties of the \textit{majorization lattice}. More precisely, we propose as approximate target state one whose Schmidt coefficients are given by the supremum between $ψ$ and $ϕ$. Our proposal is inspired on the observation that fidelity does not respect the majorization relation in general. Remarkably enough, we find that for some particular interesting cases, like two-qubit pure states or the entanglement concentration protocol, both proposals are coincident.

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。

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