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arXiv 2207.04593quant-ph
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基于端口的量子隐形传态的高维性能

Higher-dimensional performance of port-based teleportation

Zhi-Wei Wang, Samuel L. Braunstein

备注：
7 pages, Published in Scientific Reports
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摘要：

基于端口的隐形传态（PBT）是常规量子隐形传态的一种变体，它不需要最终的么正修正。然而，其行为的高维系统已很难计算明确超过尺寸$d=2$。事实上，依赖于传统的希尔伯特空间表示需要随着维数的增加而增加指数开销。一些一般的上限和下限的各种成功的措施，如（纠缠）保真度，是已知的，但有些变得微不足道的更高的维度。在这里，我们构建了一个图论代数（Temperley-Lieb代数的一个子集），它允许我们显式地计算PBT的高维性能，用于所谓的“相当好的测量”，其表示开销可以忽略不计。该图形代数允许我们显式地计算成功概率，以区分任意维度$d$和低端口数$N$的不同结果和保真度，另外获得简单的上限。低$N$和任意$d$的结果表明，对于大的$d$，保真度渐近地接近${N}/{d^2}$，证实了文献中的一个下界的性能。

英文摘要：

Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. However, its behavior for higher-dimensional systems has been hard to calculate explicitly beyond dimension $d=2$. Indeed, relying on conventional Hilbert-space representations entails an exponential overhead with increasing dimension. Some general upper and lower bounds for various success measures, such as (entanglement) fidelity, are known, but some become trivial in higher dimensions. Here we construct a graph-theoretic algebra (a subset of Temperley-Lieb algebra) which allows us to explicitly compute the higher-dimensional performance of PBT for so-called "pretty-good measurements" with negligible representational overhead. This graphical algebra allows us to explicitly compute the success probability to distinguish the different outcomes and fidelity for arbitrary dimension $d$ and low number of ports $N$, obtaining in addition a simple upper bound. The results for low $N$ and arbitrary $d$ show that the fidelity asymptotically approaches ${N}/{d^2}$ for large $d$, confirming the performance of one lower bound from the literature.

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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