Information geometry of Gaussian channels

Abstract

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 from 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 byproduct, 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 formulae 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).

19 pages, 4 figures

References in corpus (13)

• Experimental quantum teleportation
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Distance measures to compare real and ideal quantum processes
• Quantum information with Gaussian states
• Multiphoton Quantum Optics and Quantum State Engineering
• Optimal quantum estimation of loss in bosonic channels
• Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states
• Optimal phase measurements with pure Gaussian states
• Quantifying decoherence in continuous variable systems
• Unitarily localizable entanglement of Gaussian states
• Mode-Wise Entanglement of Gaussian States
• Estimation of unitary quantum operations
• Multiplicativity of maximal output purities of Gaussian channels under Gaussian inputs

Cited by in corpus (41)

• Advances in Quantum Cryptography
• Multi-parameter Quantum Metrology
• Optimal quantum estimation of the Unruh-Hawking effect
• Spectral entropies as information-theoretic tools for complex network comparison
• Optimal estimation of joint parameters in phase space
• Quantum Plasmonic Sensors
• A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry
• Multiparameter Gaussian Quantum Metrology
• Qubit thermometry for micromechanical resonators
• Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale
• Gaussian systems for quantum enhanced multiple phase estimation
• Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
• Random bosonic states for robust quantum metrology
• Quantum probes for the spectral properties of a classical environment
• Quantum-limited loss sensing: Multiparameter estimation and Bures distance between loss channels
• Bounds on Quantum Multiple-Parameter Estimation with Gaussian State
• Quantum Fisher information and symmetric logarithmic derivative via anti-commutators
• Optimal detection of losses by thermal probes
• Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach
• Quantum Fisher information on two manifolds of two-mode Gaussian states
• Multiple phase estimation in quantum cloning machines
• Multiparameter estimation perspective on non-Hermitian singularity-enhanced sensing
• Gaussian quantum estimation of the lossy parameter in a thermal environment
• Non-equilibrium readiness and accuracy of Gaussian Quantum Thermometers
• On quantum interferometric measurements of temperature
• Tunable non-Gaussian resources for continuous-variable quantum technologies
• Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources
• Geometry of the Pauli maps and Pauli channels
• Classical distinguishability as an operational measure of polarization
• Improving parameters estimation in Gaussian channels using quantum coherence
• Geometry of generalized Pauli channels
• Geometry on the manifold of Gaussian quantum channels
• Entanglement-assisted detection of fading targets via correlation-to-coherence conversion
• Stationary entanglement of photons and atoms in a high-finesse resonator
• Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
• Geometry of symmetric and non-invertible Pauli channels
• Localised Systems in Relativistic Quantum Information
• Joint estimation of phase and phase diffusion for quantum metrology
• Typical Gaussian Quantum Information
• Impact of the Unruh effect on the estimation precision of Gaussian channel parameters
• Information geometry of bosonic Gaussian thermal states