Optimal estimation of losses at the ultimate quantum limit with non-Gaussian states

TL;DR

This paper demonstrates that non-Gaussian Fock states can optimally estimate loss in quantum channels, outperforming Gaussian probes especially at low energies, and saturate the ultimate quantum limit.

Contribution

It proves Fock states achieve the ultimate loss estimation bound unconditionally and shows superpositions of low-lying Fock states improve precision over Gaussian probes.

Findings

Fock states saturate the quantum loss estimation bound for all loss values.

Superpositions of low-lying Fock states outperform Gaussian probes at low energies.

Few-photon non-Gaussian states can be constructed as truncations of de-Gaussified states.

Abstract

We address the estimation of the loss parameter of a bosonic channel probed by arbitrary signals. Unlike the optimal Gaussian probes, which can attain the ultimate bound on precision asymptotically either for very small or very large losses, we prove that Fock states at any fixed photon number saturate the bound unconditionally for any value of the loss. In the relevant regime of low-energy probes, we demonstrate that superpositions of the first low-lying Fock states yield an absolute improvement over any Gaussian probe. Such few-photon states can be recast quite generally as truncations of de-Gaussified photon-subtracted states.