Gaussian quantum estimation of the lossy parameter in a thermal environment

Abstract

Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the lossy parameter, we study the energy-constrained quantum Fisher information (QFI) for generic temperature and lossy parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum state optimizes the QFI for any value of the lossy parameter and temperature. We discuss the optimization of the {\it total} QFI, where the number of probes is allowed to vary by keeping the total energy-constrained. In this context, we elucidate the role of the "shadow-effect" for reaching a quantum advantage. We also consider a photon-number normalization for the environment, widely used in the analysis of quantum illumination and quantum reading protocols. With this normalization, we prove that the large bandwidth TMSV state is the optimal probe for any parameter value. Here, the quantum advantage is of at most a factor of $2$, and is reached in the bright environment case for {\it any} lossy parameter values. Finally, we discuss the implications of our results for quantum illumination and quantum reading applications.

References in corpus (18)

• Quantum metrology from a quantum information science perspective
• Quantum Illumination with Gaussian States
• The Quantum Chernoff Bound
• Microwave Quantum Illumination
• Quantum Illumination at the Microwave Wavelengths
• Gaussian-state quantum-illumination receivers for target detection
• Optimal quantum estimation of loss in bosonic channels
• Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
• Phase space formalism for quantum estimation of Gaussian states
• Squeezed vacuum as a universal quantum probe
• Non-Markovian quantum thermometry
• Quantum estimation of a damping constant
• Discrimination of Ohmic thermal baths by quantum dephasing probes
• A comparison between quantum and classical noise radar sources
• Optimal gain sensing of quantum-limited phase-insensitive amplifiers
• Gaussian quantum metrology in a dissipative environment

Cited by in corpus (13)

• Quantum-enhanced Doppler lidar
• Optimal Generators for Quantum Sensing
• Quantum Illumination with a Hetero-Homodyne Receiver and Sequential Detection
• Quantum-Enhanced Transmittance Sensing
• Interplay between time and energy in bosonic noisy quantum metrology
• Quantum-enhanced weak absorption estimation with correlated photons
• Quantum limits of covert target detection
• Classes of Gaussian States for Squeezing Estimation
• Not even 6 dB: Gaussian quantum illumination in thermal background
• Gaussian Quantum Illumination via Monotone Metrics
• Bayesian minimum mean square error for transmissivity sensing
• Simultaneous optical phase and loss estimation revisited: measurement and probe incompatibility
• Two-stage Quantum Estimation and the Asymptotics of Quantum-enhanced Transmittance Sensing