波形估计的量子Bell-Ziv-Zakai界和Heisenberg极限
The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
摘要：
我们提出了量子版本的Bell-Ziv-Zakai下界的错误在多参数估计。作为一个应用，我们考虑测量的时变光学相位信号与平稳高斯先验统计和幂律谱$\sim 1/|ω|^p$，与$p>1$。在没有其他假设的情况下，我们证明了均方误差有一个下限标度为$1/{\cal N}^{2(p-1)/(p+1)}$，其中${\cal N}$是时间平均的平均光子通量。此外，我们表明，这种精度是可以实现的采样和插值，任何$p>1$。因此，这个界限是一个严格的推广海森堡限制，测量一个单一的未知的光学相位，一个随机变化的光学相位。
英文摘要：
We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error in multiparameter estimation. As an application we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power law spectrum $\sim 1/|ω|^p$, with $p>1$. With no other assumptions, we show that the mean-square error has a lower bound scaling as $1/{\cal N}^{2(p-1)/(p+1)}$, where ${\cal N}$ is the time-averaged mean photon flux. Moreover, we show that this accuracy is achievable by sampling and interpolation, for any $p>1$. This bound is thus a rigorous generalization of the Heisenberg limit, for measurement of a single unknown optical phase, to a stochastically varying optical phase.
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