Variational Limits for Phase Precision in Linear Quantum Optical Metrology

Abstract

We apply the variational method to obtain the universal and analytical lower bounds for parameter precision in some noisy systems. We first derive a lower bound for phase precision in lossy optical interferometry at non-zero temperature. Then we consider the effect of both amplitude damping and phase diffusion on phase-shift precision. At last, we extend the constant phase estimation to the case of continuous fluctuating phase estimation, and find that due to photon losses the corresponding mean square error transits from the stochastic Heisenberg limit to the stochastic standard quantum limit as the total photon flux increases.

6 pages, 3 figures

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Cited by in corpus (4)

• Fisher information of a squeezed-state interferometer with a finite photon-number resolution
• Optimal Gaussian Metrology for Generic Multimode Interferometric Circuit
• Evaluating the quantum Ziv-Zakai bound in noisy environments
• Ultimate phase estimation in a squeezed-state interferometer using photon counters with a finite number resolution