随机海森堡极限：涨落相位的最佳估计
Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase
摘要：
估计施加在光束上的波动相位的最终限制可以使用最近导出的连续量子克拉美-拉奥界限。对于高斯平稳统计，以及相位谱渐近缩放为1/ω ^p且p> 1，任何（单次）相位估计的最小均方误差缩放为N ^{-2（p-1）/（p +1）}，其中N是光子通量。这给出了常相位的通常海森堡极限（作为极限p->无穷大），并提供了波动相位的随机海森堡极限。对于p = 2（布朗运动），这个极限可以通过相位跟踪来达到。
英文摘要：
The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as 1/omega^p with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p--> infinity) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.
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