Quantum-limited loss sensing: Multiparameter estimation and Bures distance between loss channels

TL;DR

This paper derives optimal strategies for estimating multiple loss parameters in optical systems under energy constraints, revealing that certain pure states achieve quantum limits and providing explicit measures of channel distinguishability.

Contribution

It introduces a general framework for multiparameter loss estimation with energy constraints and identifies optimal probes and measurements, including the surprising optimality of number-diagonal states.

Findings

Pure number-diagonal states achieve the quantum Fisher information bound.

Two-mode squeezed vacuum probes with minimal squeezing are optimal.

Explicit calculation of Bures distance between loss channels.

Abstract

The problem of estimating multiple loss parameters of an optical system using the most general ancilla-assisted parallel strategy is solved under energy constraints. An upper bound on the quantum Fisher information matrix is derived assuming that the environment modes involved in the loss interaction can be accessed. Any pure-state probe that is number-diagonal in the modes interacting with the loss elements is shown to exactly achieve this upper bound even if the environment modes are inaccessible, as is usually the case in practice. We explain this surprising phenomenon, and show that measuring the Schmidt bases of the probe is a parameter-independent optimal measurement. Our results imply that multiple copies of two-mode squeezed vacuum probes with an arbitrarily small nonzero degree of squeezing, or probes prepared using single-photon states and linear optics can achieve quantum-optimal performance in conjunction with on-off detection. We also calculate explicitly the energy-constrained Bures distance between any two product loss channels. Our results are relevant to standoff image sensing, biological imaging, absorption spectroscopy, and photodetector calibration.