Kukulski Ryszard, Stępniak Mateusz, Hendzel Kamil, Pawela Łukasz, Gardas Bartłomiej, Puchała Zbigniew
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland.
Quantumz.io Sp. z o.o., Puławska 12/3, 02-566, Warsaw, Poland.
Sci Rep. 2024 Nov 4;14(1):26588. doi: 10.1038/s41598-024-75148-z.
In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.
在这项工作中，我们分析了酉量子信道的局部认证，它是量子假设检验的自然扩展。我们考虑了一种特殊情况，即量子信道作用于两个系统，输入对应于积态。目标是在给定第一类错误的指定最大概率的情况下，通过与辅助系统纠缠来辅助，使第二类错误的概率最小化。我们的结果表明了局部认证问题与酉矩阵的积数值域之间的联系。我们证明了最优局部策略不需要使用辅助系统，只需要一轮单向经典通信。此外，我们比较了局部和全局认证策略，结果表明通常局部策略是最优的，但在某些极端情况下，全局策略不会出错，而局部策略可能会惨败。最后，我们还讨论了冯·诺依曼测量的局部认证的一些应用。
