Quantum parameter estimation using general single-mode Gaussian states

Abstract

We calculate the quantum Cramér--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian states. We apply the formula to the problems of estimating phase, purity, loss, amplitude, and squeezing. In the case of the simultaneous measurement of several parameters, we provide the full quantum Fisher information matrix. Our results unify previously known partial results, and constitute a complete solution to the problem of knowing the best possible sensitivity of measurements based on a single-mode Gaussian state.

References in corpus (17)

• Gaussian Quantum Information
• Generalized uncertainty relations: Theory, examples, and Lorentz invariance
• Quantum information with Gaussian states
• Quantum Enhanced Multiple Phase Estimation
• Optimal quantum estimation of loss in bosonic channels
• Optimal phase measurements with pure Gaussian states
• Uhlmann fidelity between two-mode Gaussian states
• Optimal estimation of joint parameters in phase space
• Fidelity for displaced squeezed states and the oscillator semigroup
• Ultimate sensitivity of precision measurements with Gaussian quantum light : a multi-modal approach
• Phase estimation for thermal Gaussian states
• Homodyne estimation of Gaussian quantum discord
• Optimal estimation of entanglement
• Bures and Statistical Distance for Squeezed Thermal States
• Bures distance between two displaced thermal states
• Experimental demonstration of frequency-degenerate bright EPR beams with a self-phase-locked optical parametric oscillator
• Optimal estimation of squeezing

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