2009/11/30 by Alex Monràs, Alex Monras, Fabrizio Illuminati · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Combinatorics #Covariance #Fisher information #Gaussian #Geometry #Information geometry #Mathematics #Metric (unit) #Metric tensor #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Quantum state #Statistical physics #Statistics #Topology (electrical circuits) #cond-mat.other #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.81.062326
published as Phys. Rev. A 81, 062326 (2010) · 19 pages, 4 figures
arxiv created 2010/03/22 · openalex publication_date 2010/06/21 · arxiv updated 2015/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).