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

Understand

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.