论文标题
基于端口的传送的高维度
Higher-dimensional performance of port-based teleportation
论文作者
论文摘要
基于端口的传送（PBT）是常规量子传送的一种变体，无需最终的统一校正。但是，它对高维系统的行为很难明确计算超出尺寸$ d = 2 $。实际上，依靠传统的希尔伯特空间表示形式需要随着尺寸的增加指数开销。已知的各种成功指标的一般上限和下限是（例如（纠缠）保真度），但有些在更高的维度上变得微不足道。在这里，我们构建了一个图理论代数（temberley-lieb代数的子集），该代数使我们能够明确计算PBT的较高尺寸性能，以用可忽略的代表性间接开销，以实现所谓的“漂亮的测量”。该图形代数使我们能够明确计算成功的概率，以区分任意维度$ d $和端口数量$ n $的不同结果和保真度，并获得了一个简单的上限。低$ n $和任意$ d $的结果表明，对于大$ d $的忠诚度渐近接近$ {n}/{d^2} $，这证实了文献中一个下层的性能。
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.
