Phase Estimation with Non-Unitary Interferometers: Information as a Metric

TL;DR

This paper develops a formalism to analyze phase estimation in quantum interferometers considering real-world imperfections like losses, non-deterministic state preparation, and detection inefficiencies, and evaluates their impact on information metrics.

Contribution

It introduces a general expression for measurement probabilities incorporating non-idealities and applies it to analyze Fisher information and fidelity in lossy interferometers with specific quantum states.

Findings

Losses and imperfections reduce Fisher information and fidelity.

Phase estimation performance depends on the true phase value.

Non-idealities cause qualitative differences in phase estimation outcomes.

Abstract

Determining the phase in one arm of a quantum interferometer is discussed taking into account the three non-ideal aspects in real experiments: non-deterministic state preparation, non-unitary state evolution due to losses during state propagation, and imperfect state detection. A general expression is written for the probability of a measurement outcome taking into account these three non-ideal aspects. As an example of applying the formalism, the classical Fisher information and fidelity (Shannon mutual information between phase and measurements) are computed for few-photon Fock and N00N states input into a lossy Mach-Zehnder interferometer. These three non-ideal aspects lead to qualitative differences in phase estimation, such as a decrease in fidelity and Fisher information that depends on the true value of the phase.