Noncommuting observables in quantum detection and estimation theory
Noncommuting observables in quantum detection and estimation theory
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DOI：
10.1109/tit.1974.1055173
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
C. Helstrom;R. Kennedy
中科院分区：
文献类型：
--
作者：
C. Helstrom;R. Kennedy
基于量子接收器中非对易可观测量的同时近似测量进行决策和估计被证明等效于在比接收器本身更大的希尔伯特空间上测量对易投影算子。比较了由密度算符的右对数导数和对称化对数导数导出的量子力学Cramer-Rao不等式，证明了后者给出了相干信号到达时间和载波频率的个体无偏估计的误差方差的上级下界.对于同时估计的误差方差的适当加权和，在一定条件下，前者产生上级下界。
Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.