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 energyconstrained 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 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 any lossy parameter values. Finally, we discuss the implications of our results for quantum illumination and quantum reading applications.

Optimal Gain Sensing of Quantum-Limited Phase-Insensitive Amplifiers

“…Beyond gain sensing itself, owing to the above-mentioned concatenation theorem, our results combined with those for pure-loss channels [11] are expected to yield fundamental performance limits for a vast suite of detection and estimation problems involving Gaussian channels with excess noise-see, e.g., Refs. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Quantum-Enhanced Transmittance Sensing

“…Although it has been shown to be an optimal Gaussian state for all values of η, nB , and nS [27], characterization of a general quantum input state that maximizes QFI associated with η is an open problem. That being said, as mentioned in Section I, the low photon number per mode regime is important for the design of sensors operating under the total power constraints.…”

“…However, [21] leaves open the structure of ρI n S n that saturates (1), and the design of the measurement that achieves the corresponding quantum CRB. Recent work [27] investigates transmittance sensing using Gaussian states [19] and with and without noise aiding the estimation. While their treatment of QFI is comprehensive, they do not consider receiver structures that achieve QFI.…”