论文标题
简单的上限和下边界在区分任意有限维量子过程的最终成功概率上
Simple upper and lower bounds on the ultimate success probability for discriminating arbitrary finite-dimensional quantum processes
论文作者
论文摘要
我们考虑区分有限维量子过程（也称为量子超图）的问题，该过程可以由多个时间步骤组成。获得歧视量子过程的最终绩效至关重要，但主要是由于需要考虑量子力学允许的所有歧视策略，包括纠缠辅助策略和适应性策略。如果要歧视的过程具有内部记忆，那么最终的绩效通常会更难分析。在本文中，我们对区分任意量子过程的最终成功概率提出了一个简单的上限。在多光通道歧视的特殊情况下，可以表明，如果通道评估的数量增加一个，则最终成功概率最多会增加由给定通道确定的恒定因子。我们还根据贝叶斯更新提供了一个下限，该更新的计算成本较低。我们的数值实验表明，所提出的边界相当紧。所提出的边界不明确取决于任何量子现象，并且可以很容易地扩展到一般的操作概率理论。
We consider the problem of discriminating finite-dimensional quantum processes, also called quantum supermaps, that can consist of multiple time steps. Obtaining the ultimate performance for discriminating quantum processes is of fundamental importance, but is challenging mainly due to the necessity of considering all discrimination strategies allowed by quantum mechanics, including entanglement-assisted strategies and adaptive strategies. In the case in which the processes to be discriminated have internal memories, the ultimate performance would generally be more difficult to analyze. In this paper, we present a simple upper bound on the ultimate success probability for discriminating arbitrary quantum processes. In the special case of multi-shot channel discrimination, it can be shown that the ultimate success probability increases by at most a constant factor determined by the given channels if the number of channel evaluations increases by one. We also present a lower bound based on Bayesian updating, which has a low computational cost. Our numerical experiments demonstrate that the proposed bounds are reasonably tight. The proposed bounds do not explicitly depend on any quantum phenomena, and can be readily extended to a general operational probabilistic theory.
