Joint estimation of real squeezing and displacement

Abstract

We study the problem of joint estimation of real squeezing and amplitude of the radiation field, deriving the measurement that maximizes the probability density of detecting the true value of the unknown parameters. More generally, we provide a solution for the problem of estimating the unknown unitary action of a nonunimodular group in the maximum likelihood approach. Remarkably, in this case the optimal measurements do not coincide with the so called square-root measurements. In the case of squeezing and displacement we analyze in detail the sensitivity of estimation for coherent states and displaced squeezed states, deriving the asymptotic relation between the uncertainties in the joint estimation and the corresponding uncertainties in the optimal separate measurements of squeezing and displacement. A two-mode setup is also analyzed, showing how entanglement between optical modes can be used to approximate perfect estimation.

14 pages, 3 eps figures; a section has been added with new results in terms of Heisenberg uncertainty relations for the joint measurement

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• Multi-parameter Quantum Metrology
• Optimal estimation of joint parameters in phase space
• Precision quantum metrology and nonclassicality in linear and nonlinear detection schemes
• Multiple phase estimation in quantum cloning machines
• Optical estimation of unitary Gaussian processes without phase reference using Fock states
• Multiparameter estimation with two qubit probes in noisy channels
• Joint estimation of phase and phase diffusion for quantum metrology