## Abstract

The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramér-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as ω^{-}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→∞) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.

Original language | English |
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Article number | 113601 |

Pages (from-to) | 1-5 |

Number of pages | 5 |

Journal | Physical Review Letters |

Volume | 111 |

Issue number | 11 |

DOIs | |

Publication status | Published - 13 Sep 2013 |