### 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.

Language | English |
---|---|

Article number | 113601 |

Pages | 1-5 |

Number of pages | 5 |

Journal | Physical Review Letters |

Volume | 111 |

Issue number | 11 |

DOIs | |

Publication status | Published - 13 Sep 2013 |

### Fingerprint

### Bibliographical note

Berry, D. W., Hall, M. J. W., & Wiseman, H. M. (2013). Stochastic heisenberg limit : optimal estimation of a fluctuating phase. Physical review letters, 111(11), 113601, 2013. Copyright 2013 by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevLett.111.113601### Cite this

*Physical Review Letters*,

*111*(11), 1-5. [113601]. https://doi.org/10.1103/PhysRevLett.111.113601

}

*Physical Review Letters*, vol. 111, no. 11, 113601, pp. 1-5. https://doi.org/10.1103/PhysRevLett.111.113601

**Stochastic heisenberg limit : optimal estimation of a fluctuating phase.** / Berry, Dominic W.; Hall, Michael J W; Wiseman, Howard M.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Stochastic heisenberg limit

T2 - Physical Review Letters

AU - Berry, Dominic W.

AU - Hall, Michael J W

AU - Wiseman, Howard M.

N1 - Berry, D. W., Hall, M. J. W., & Wiseman, H. M. (2013). Stochastic heisenberg limit : optimal estimation of a fluctuating phase. Physical review letters, 111(11), 113601, 2013. Copyright 2013 by the American Physical Society. The original article can be found at http://dx.doi.org/10.1103/PhysRevLett.111.113601

PY - 2013/9/13

Y1 - 2013/9/13

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84884230444&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.111.113601

DO - 10.1103/PhysRevLett.111.113601

M3 - Article

VL - 111

SP - 1

EP - 5

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 11

M1 - 113601

ER -