量子参数估计的下界
Lower Bounds for Quantum Parameter Estimation
摘要：
量子力学定律对测量的准确性以及对量子系统未知参数的估计都有基本的限制。在这项工作中，我们证明了置信区域的大小的下限报告的任何区域估计为一个给定的合奏探测状态和成功的概率。我们的界限来自以前未注意到的置信区域的大小和相应的二进制假设检验的错误概率之间的连接。在群协变的情况下，我们发现，有一个最终的界限，任何估计方案只依赖于代表理论的数据的探针系统，我们评估其渐近的限制，许多系统，建立一个一般的“海森堡极限”的区域估计。我们将我们的结果应用到几个例子中，特别是相位估计，我们的边界使我们能够恢复著名的海森堡和散粒噪声缩放。
英文摘要：
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported by any region estimator for a given ensemble of probe states and probability of success. Our bounds are derived from a previously unnoticed connection between the size of confidence regions and the error probabilities of a corresponding binary hypothesis test. In group-covariant scenarios, we find that there is an ultimate bound for any estimation scheme which depends only on the representation-theoretic data of the probe system, and we evaluate its asymptotics in the limit of many systems, establishing a general "Heisenberg limit" for region estimation. We apply our results to several examples, in particular to phase estimation, where our bounds allow us to recover the well-known Heisenberg and shot-noise scaling.
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