Bounding the quantum limits of precision for phase estimation with loss and thermal noise

Christos N. Gagatsos, Boulat A. Bash, Saikat Guha, and Animesh Datta
Phys. Rev. A 96, 062306 – Published 4 December 2017

Abstract

We consider the problem of estimating an unknown but constant carrier phase modulation θ using a general, possibly entangled, n-mode optical probe through n independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating θ as a function of n, the mean and variance of the total number of photons NS in the n-mode probe, the transmissivity η, and mean thermal photon number per mode n¯B of the bosonic channel. Since the inverse of QFI provides a lower bound to the mean-square error (MSE) of an unbiased estimator θ̃ of θ, our upper bound to the QFI provides a lower bound to the MSE. It already has found use in proving fundamental limits of covert sensing and could find other applications requiring bounding the fundamental limits of sensing an unknown parameter embedded in a correlated field.

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  • Received 2 October 2017

DOI:https://doi.org/10.1103/PhysRevA.96.062306

©2017 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyAtomic, Molecular & Optical

Authors & Affiliations

Christos N. Gagatsos1, Boulat A. Bash2, Saikat Guha2,3, and Animesh Datta1

  • 1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
  • 2Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, Massachusetts 02138, USA
  • 3College of Optical Sciences, University of Arizona, 1630 East University Boulevard, Tucson, Arizona 85719, USA

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Issue

Vol. 96, Iss. 6 — December 2017

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