贝叶斯量子参数估计策略优化：自适应贪心、并行、顺序及通用策略
Strategy optimization for Bayesian quantum parameter estimation with finite copies: Adaptive greedy, parallel, sequential, and general strategies
AI总结：
本文提出了一种基于高阶操作的算法，用于优化贝叶斯量子参数估计策略，在不同类别中比较了最优贝叶斯得分，并展示了算法在单参数和多参数估计中的有效性。
摘要：
在本工作中，我们研究了在有限次数使用过程中编码一个或多个未知物理量的情况下，贝叶斯量子参数估计的问题。对于多次使用的情况，通常将量子计量协议分为并行、顺序或不定因果顺序。在每种类别中，核心问题是确定最优策略——即选择最优的输入状态、控制操作、测量和估计器——以完成估计任务。利用高阶操作的公式化方法，我们开发了一种寻找最优解的算法，并基于半定规划提供了高效的数值实现。我们的基准示例，特别是与现有解析解的对比，展示了我们的方法多么强大和精确。我们进一步探索了基于经典前馈的自适应贪心策略的潜力，以设计下一步的最优协议。使用这一框架，我们比较了不同类别中可实现的最优贝叶斯得分。我们通过多个示例展示了算法的强度，从单参数估计到多参数估计，以及各种先验分布。特别地，我们发现不同类别之间存在严格的等级关系。然而，不同量子内存辅助类别的性能并无显著差异，但它们可能显著优于自适应贪心策略。
英文摘要：
In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. We analyze the performance of different kinds of quantum metrological protocols, including the conventional parallel, sequential, or general, which may involve an indefinite causal order. We also analyze a class of hybrid adaptive greedy strategies, which are based on classical feedforward between quantum protocols to optimize the next round. Within each class, the central question is to determine the optimal strategy -- namely, the choice of optimal input state, control operations, measurement, and estimators. Using the formalism of higher-order operations, we develop an algorithm that searches for the optimal solution, and we provide a numerical implementation based on semidefinite programming. Our benchmark cases, specifically those against existing analytical solutions, demonstrate how powerful and precise our method is. We further demonstrate the strength of our algorithm in several examples, from single to multiparameter estimation, and with various prior distributions. Particularly, we find examples where the adaptive greedy strategy matches the performance of general strategies with indefinite causal order, and at the same time examples that showcase a strict hierarchy between all different classes.
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