DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB30WA, UK.
Institute for Theoretical Physics, University of Wrocław, 50-204, Wrocław, Poland.
Sci Rep. 2017 Sep 7;7(1):10871. doi: 10.1038/s41598-017-10051-4.
Port-based teleportation (PBT), introduced in 2008, is a type of quantum teleportation protocol which transmits the state to the receiver without requiring any corrections on the receiver's side. Evaluating the performance of PBT was computationally intractable and previous attempts succeeded only with small systems. We study PBT protocols and fully characterize their performance for arbitrary dimensions and number of ports. We develop new mathematical tools to study the symmetries of the measurement operators that arise in these protocols and belong to the algebra of partially transposed permutation operators. First, we develop the representation theory of the mentioned algebra which provides an elegant way of understanding the properties of subsystems of a large system with general symmetries. In particular, we introduce the theory of the partially reduced irreducible representations which we use to obtain a simpler representation of the algebra of partially transposed permutation operators and thus explicitly determine the properties of any port-based teleportation scheme for fixed dimension in polynomial time.
基于端口的量子隐形传态（Port-based teleportation，PBT）于 2008 年提出，是一种量子隐形传态协议，它在不要求接收器进行任何校正的情况下将量子态传输到接收器。评估 PBT 的性能在计算上是难以处理的，之前的尝试仅在小系统上取得了成功。我们研究了 PBT 协议，并对任意维度和端口数量的协议性能进行了全面描述。我们开发了新的数学工具来研究这些协议中出现的测量算子的对称性，这些对称性属于部分转置排列算子的代数。首先，我们发展了所提到的代数的表示理论，这为理解具有一般对称性的大系统子系统的性质提供了一种优雅的方法。特别是，我们引入了部分约化不可约表示理论，我们用它来获得部分转置排列算子代数的更简单表示，从而可以在多项式时间内显式确定任何固定维度的基于端口的隐形传态方案的性质。
