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arXiv quant-ph/0401187quant-ph
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局部可观测量的量子估计

Quantum Estimation by Local Observables

M. Hotta, M. Ozawa

摘要:

量子估计理论提供了各种估计问题的未知参数的状态下的系统的最佳观察。然而,该理论是在假设每个可观察对象都可供实验者使用的前提下发展起来的。在这里,我们将理论推广到实验者只能使用局部可达观测量的问题。对于这类问题,我们通过得到Fisher信息的显式形式作为局部可达观测量估计的均方误差的倒数下界,建立了一个Cram{é}r-Rao型不等式.此外,我们探讨了各种局部量子估计问题的复合系统,其中非平凡的组合数学是需要获得的Fisher信息。

英文摘要:

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable is available for experimenters. Here, we generalize the theory to problems in which the experimenter can use only locally accessible observables. For such problems, we establish a Cram{é}r-Rao type inequality by obtaining an explicit form of the Fisher information as a reciprocal lower bound for the mean square errors of estimations by locally accessible observables. Furthermore, we explore various local quantum estimation problems for composite systems, where non-trivial combinatorics is needed for obtaining the Fisher information.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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