量子参数估计的Ziv-Zakai误差界
Ziv-Zakai Error Bounds for Quantum Parameter Estimation
摘要：
我提出量子版本的Ziv-Zakai界替代广泛使用的量子Cramér-Rao界的量子参数估计。从一个简单的形式提出的界限，我得到了一个“海森堡”的误差限制，规模与平均能量和限制类似的量子克拉美-拉奥界，规模与能量方差。这些结果进一步说明了应用的约束的几个例子的光学相位估计，这表明，量子Ziv-Zakai界可以更高，因此比量子克拉默-拉奥界具有高度非高斯光子数统计在某些制度的状态，也保持接近后者的地方，后者预计是紧。
英文摘要：
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cramér-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that scales with the average energy and a limit similar to the quantum Cramér-Rao bound that scales with the energy variance. These results are further illustrated by applying the bound to a few examples of optical phase estimation, which show that a quantum Ziv-Zakai bound can be much higher and thus tighter than a quantum Cramér-Rao bound for states with highly non-Gaussian photon-number statistics in certain regimes and also stay close to the latter where the latter is expected to be tight.
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