Dominic W. Berry, Michael J. W. Hall, Howard M. Wiseman
The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cram\'er-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as \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.
View original:
http://arxiv.org/abs/1306.1279
No comments:
Post a Comment