Quantum phase estimation with lossy interferometers

TL;DR

This paper investigates optimal quantum states for optical interferometry under photon loss, deriving formulas for phase estimation precision and demonstrating quantum advantage over classical methods, while analyzing various input states.

Contribution

It provides analytical formulas for quantum phase estimation precision with photon loss and proves the optimality of certain quantum states, advancing understanding of quantum metrology.

Findings

Quantum states can beat the standard quantum limit in lossy interferometers.

Optimal precision is obtained through convex optimization.

States with indefinite photon number or distributed in time do not improve precision.

Abstract

We give a detailed discussion of optimal quantum states for optical two-mode interferometry in the presence of photon losses. We derive analytical formulae for the precision of phase estimation obtainable using quantum states of light with a definite photon number and prove that maximization of the precision is a convex optimization problem. The corresponding optimal precision, i.e. the lowest possible uncertainty, is shown to beat the standard quantum limit thus outperforming classical interferometry. Furthermore, we discuss more general inputs: states with indefinite photon number and states with photons distributed between distinguishable time bins. We prove that neither of these is helpful in improving phase estimation precision.