N00N states — maximally entangled states of N photons that are all in one arm or all in the other arm of an interferometer — achieve phase sensitivity that scales as 1/N, beating the classical 1/√N limit. In theory, this is the ultimate quantum advantage for interferometry. In practice, photon loss destroys the entanglement and erases the advantage.
Dalidet et al. (arXiv:2603.13144) work out the full theory of partially entangled N00N states in a folded Franson interferometer with realistic imperfections: asymmetric losses (different loss rates in the two arms) and input imbalance (unequal splitting at the beam splitter). They derive closed-form expressions for fringe visibility and Fisher information — the two quantities that determine interferometric performance.
The key finding: perfect interference contrast can always be recovered by compensating loss asymmetry with deliberate input imbalance. If one arm loses more photons, you send more photons into that arm. The visibility returns to unity regardless of the loss magnitude. But the Fisher information — the actual measurement sensitivity — peaks at a different operating point than perfect visibility. The settings that maximize contrast are not the settings that maximize information.
This decoupling of visibility and sensitivity changes how N00N-state experiments should be optimized. Previous work maximized fringe visibility as a proxy for performance. The closed-form Fisher information shows that the optimal strategy under asymmetric loss is not to equalize the output but to accept reduced visibility in exchange for higher sensitivity. The critical loss thresholds and minimum entanglement levels for genuine quantum advantage over single-photon strategies are derived as functions of N, completing the practical roadmap.