Robustness and optimization of N00N-state interferometry

TL;DR

This paper analyzes the effects of losses and input imbalance on N00N-state interferometry, providing exact formulas for visibility and Fisher information, and identifies conditions for quantum advantage over single-photon strategies.

Contribution

It offers a comprehensive theoretical framework for optimizing N00N-state interferometry considering realistic imperfections and benchmarks quantum advantage under loss conditions.

Findings

Perfect interference contrast can be restored by compensating loss asymmetry.

Fisher information peaks at a different point than visibility, indicating a trade-off.

Quantum advantage requires minimum entanglement and is affected by loss scaling with photon number N.

Abstract

Quantum-enhanced interferometry is often discussed in terms of ideal resources and asymptotic scalings, whereas in practice its performance is set by a delicate interplay between losses, state imbalance, and photon number. We address this interplay in a folded Franson interferometer fed with partially entangled N00N states, treating asymmetric losses and tunable input imbalance on equal footing. From exact detection probabilities we obtain closed-form expressions for the fringe visibility and the Fisher information, and show that these two figures of merit respond very differently to imperfections. In particular, we demonstrate that perfect interference contrast can always be recovered by compensating loss asymmetry with an appropriate input imbalance, while the Fisher information generally peaks at a distinct operating point, reflecting the irreducible trade-off between coherence restoration and signal attenuation. By determining the exact optima and benchmarking against single-photon strategies, we identify the critical loss and minimum entanglement required to maintain a genuine quantum advantage over optimized single-photon strategies under identical loss conditions, and establish their scaling with the photon number N . Beyond delineating the fundamental trade-offs between loss, entanglement, and sensitivity, this work establishes a comprehensive theoretical framework that both underpins and extends the experimental demonstration of quantum advantage reported in [1], providing a unified description of the relevant operating regimes.