AI 中文总结
本文研究后选择计量学的不确定度极限，发现后选择QFI对应的条件生成元不确定度与Ozawa-Hall不确定度等价，其反常不确定度可解释后选择计量学的极端灵敏度。
AI 中文摘要
对于幺正变换，纯态的量子费舍尔信息（QFI）由该态中生成元的不确定度给出。在后选择计量学中，QFI由描述生成元条件量子统计的修正表达式给出。本文表明，由后选择QFI定义的条件生成元不确定度对应于量子测量理论分析中已知的Ozawa-Hall不确定度。后选择测量结果会根据该结果的量子统计更新生成元不确定度。由于后选择倾向于将初始生成元不确定度的最大部分集中在后选择测量的低概率结果中，QFI可以超出生成元本征值的最大不确定度，这种反常的条件不确定度解释了后选择计量学中可实现的极端灵敏度。
英文摘要
For unitary transformations, the quantum Fisher information (QFI) of a pure state is given by the uncertainty of the generator in that state. In post-selected metrology, the QFI is given by a modified expression describing conditional quantum statistics of the generator. Here, we show that the conditional generator uncertainties defined by post-selected QFI correspond to Ozawa-Hall uncertainties known from the theoretical analysis of quantum measurements. The post-selected measurement outcome updates the generator uncertainty according to the quantum statistics of that outcome. Enhancements of QFI beyond the maximal uncertainties of the generator eigenvalues are possible because post-selection tends to concentrate the largest part of the initial generator uncertainty in low probability outcomes of the post-selection measurement. Anomalous conditional uncertainties thus explain the extreme sensitivities that can be achieved in post-selected metrology.
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