Homodyne detection is optimal for quantum interferometry with path-entangled coherent states

TL;DR

This paper demonstrates that homodyne detection schemes are optimal for quantum interferometry with path-entangled states, achieving the quantum Cramér-Rao bound without photon-number resolving detectors, and are robust to phase-independent performance under photon loss.

Contribution

It introduces homodyne measurement schemes that are optimal for phase estimation in quantum interferometry with entangled coherent states, avoiding the need for photon-number resolving detectors.

Findings

Homodyne schemes saturate the quantum Cramér-Rao bound.

Performance remains phase-independent even with photon loss.

Schemes do not require prior phase information or adaptive strategies.

Abstract

We present measurement schemes that do not rely on photon-number resolving detectors, but that are nevertheless optimal for estimating a differential phase shift in interferometry with either an entangled coherent state or a qubit-which-path state (where the path taken by a coherent-state wavepacket is entangled with the state of a qubit). The homodyning schemes analyzed here achieve optimality (saturate the quantum Cram\'er-Rao bound) by maximizing the sensitivity of measurement outcomes to phase-dependent interference fringes in a reduced Wigner distribution. In the presence of photon loss, the schemes become suboptimal, but we find that their performance is independent of the phase to be measured. They can therefore be implemented without any prior information about the phase and without adapting the strategy during measurement, unlike strategies based on photon-number parity measurements or direct photon counting.