The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity, and we evaluate their performance using simulators of quantum computers. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as "quantum combs"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate these algorithms by using a variational approach with parameterized quantum circuits and find that they converge well for the examples that we consider.

翻译：量子信息处理协议的性能最终由量化量子信息实际结果如何区别的可辨别措施与理想情况相比来判断。最突出的可辨别措施是那些基于真实性和痕量距离的可辨别措施,因为它们的物理解释。在本文中,我们提出并审查几种算法,以根据痕量距离和真实性估计可辨别性措施,我们使用量子计算机模拟器来评估其性能。这些算法可用于区分量子状态、渠道和战略(最后一个在文献中也称为“quantum 梳子 ” )。基于忠诚的算法对这些可辨别措施提供了新的物理解释,即单个验证人(或相互竞争的证明人)能够说服核查人接受相关计算结果的最大概率。我们用参数化量子电路的变法模拟这些算法,发现这些算法与我们所考虑的例子非常一致。