论文标题
量子计量学中普遍有条件期望的操作含义
Operational meanings of a generalized conditional expectation in quantum metrology
论文作者
论文摘要
最近出现了对量子力学的普遍条件期望（GCE）的统一形式主义，但其对可观察到的量子回顾的物理意义仍然存在争议。为了解决争议，在这里，我在量子参数估计的背景下为GCE的版本提供了操作含义。当量子传感器因腐蚀性损坏时，发现GCE会在拆卸之前和之后关联操作员值的最佳估计器。此外，由破裂引起的误差增加或遗憾被证明等于两个估计器之间的差异。真正的弱价值作为GCE的特殊情况在次优估计中起着相同的作用 - 它与最佳估计器的差异完全是不使用最佳测量值的遗憾。对于GCE的应用，我表明它可以使用动态编程来设计最小化估计误差的控制器。对于频繁的设置，我表明GCE会导致量子rao-blackwell定理，该定理对量子计量学和热光感应尤其具有重要意义。这些结果使GCE和相关的差异在量子决策和控制理论中是自然，有用且无可争议的作用。
A unifying formalism of generalized conditional expectations (GCEs) for quantum mechanics has recently emerged, but its physical implications regarding the retrodiction of a quantum observable remain controversial. To address the controversy, here I offer operational meanings for a version of the GCEs in the context of quantum parameter estimation. When a quantum sensor is corrupted by decoherence, the GCE is found to relate the operator-valued optimal estimators before and after the decoherence. Furthermore, the error increase, or regret, caused by the decoherence is shown to be equal to a divergence between the two estimators. The real weak value as a special case of the GCE plays the same role in suboptimal estimation -- its divergence from the optimal estimator is precisely the regret for not using the optimal measurement. For an application of the GCE, I show that it enables the use of dynamic programming for designing a controller that minimizes the estimation error. For the frequentist setting, I show that the GCE leads to a quantum Rao-Blackwell theorem, which offers significant implications for quantum metrology and thermal-light sensing in particular. These results give the GCE and the associated divergence a natural, useful, and incontrovertible role in quantum decision and control theory.
