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Abstract: We define a local Riemannian metric tensor in the manifold of Gaussianchannels and the distance that it induces. We adopt an information-geometricapproach and define a metric derived from the Bures-Fisher metric for quantumstates. The resulting metric inherits several desirable properties from theBures-Fisher metric and is operationally motivated from distinguishabilityconsiderations: It serves as an upper bound to the attainable quantum Fisherinformation for the channel parameters using Gaussian states, under genericconstraints on the physically available resources. Our approach naturallyincludes the use of entangled Gaussian probe states. We prove that the metricenjoys some desirable properties like stability and covariance. As a byproduct,we also obtain some general results in Gaussian channel estimation that are thecontinuous-variable analogs of previously known results in finite dimensions.We prove that optimal probe states are always pure and bounded in the number ofancillary modes, even in the presence of constraints on the reduced state inputin the channel. This has experimental and computational implications: It limitsthe complexity of optimal experimental setups for channel estimation andreduces the computational requirements for the evaluation of the metric:Indeed, we construct a converging algorithm for its computation. We provideexplicit formulae for computing the multiparametric quantum Fisher informationfor dissipative channels probed with arbitrary Gaussian states, and provide theoptimal observables for the estimation of the channel parameters e.g. bathcouplings, squeezing, and temperature.

Author: Alex Monras, Fabrizio Illuminati


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