We study a broad class of quantum process discrimination problems that can handle many optimization strategies such as the Bayes, Neyman-Pearson, and unambiguous strategies, where each process can consist of multiple time steps and can have an internal memory. Given a collection of candidate processes, our task is to find a discrimination strategy, which may be adaptive and/or entanglement assisted, that maximizes a given objective function subject to given constraints. Our problem can be formulated as a convex problem. Its Lagrange dual problem with no duality gap and necessary and sufficient conditions for an optimal solution are derived. We also show that if a problem has a certain symmetry and at least one optimal solution exists, then there also exists an optimal solution with the same type of symmetry. A minimax strategy for a process discrimination problem is also discussed. As applications of our results, we provide some problems in which an adaptive strategy is not necessary for optimal discrimination. We also present an example of single-shot channel discrimination for which an analytical solution can be obtained.

中文翻译：

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广义量子过程判别问题

我们研究了一大类量子过程判别问题，这些问题可以处理许多优化策略，例如贝叶斯、Neyman-Pearson 和明确策略，其中每个过程可以由多个时间步组成并且可以具有内部记忆。给定一组候选进程，我们的任务是找到一种判别策略，该策略可能是自适应和/或纠缠辅助的，在给定的约束下最大化给定的目标函数。我们的问题可以表述为一个凸问题。推导出其无对偶间隙的拉格朗日对偶问题和最优解的充要条件。我们还表明，如果一个问题具有一定的对称性，并且至少存在一个最优解，那么也存在一个具有相同对称类型的最优解。还讨论了过程判别问题的极小极大策略。作为我们结果的应用，我们提供了一些问题，在这些问题中，最优区分不需要自适应策略。我们还提供了一个单次通道鉴别的例子，可以获得解析解。