Multiparameter quantum estimation theory in quantum Gaussian states

Abstract

Multiparameter quantum estimation theory aims to determine simultaneously the ultimate precision of all parameters contained in the state of a given quantum system. Determining this ultimate precision depends on the quantum Fisher information matrix (QFIM) which is essential to obtaining the quantum Cramér-Rao bound. This is the main motivation of this work which concerns the computation of the analytical expression of the QFIM. Inspired by the results reported in J. Phys. A 52, 035304 (2019), the general formalism of the multiparameter quantum estimation theory of quantum Gaussian states in terms of their first and second moments is given. We give the analytical formulas of right logarithmic derivative (RLD) and symmetric logarithmic derivative (SLD) operators. Then we derive the general expressions of the corresponding quantum Fisher information matrices. We also derive an explicit expression of the condition which ensures the saturation of the quantum Cramér-Rao bound in estimating several parameters. Finally, we examine some examples to clarify the use of our results.

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Bayesian parameter estimation using Gaussian states and measurements

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Understanding and Improving Critical Metrology. Quenching Superradiant Light-Matter Systems Beyond the Critical Point

“…This means that all the information about the state is contained in the mean and variance of quadrature measurements on the wavefunction. As the initial wavefunction has a mean value equal to 0 and is subsequently being squeezed without any displacement, all the information is then stored in the variance [65,66]. As a consequence, measuring the second moment of the quadrature and using it as an estimator allows us to replace the classical Fisher information formula from Eq.…”