Extend the certification framework beyond collision-free and discrete-variable inputs

Extend the multiphoton indistinguishability certification framework beyond collision-free inputs with one photon per occupied mode and to continuous-variable states, including the states used in Gaussian boson sampling, thereby resolving the explicitly open extension identified by the authors.

Background

The paper develops certification protocols for an N-photon state with exactly one photon in each of N occupied spatial modes. The randomized protocol estimates the fidelity to the closest perfectly indistinguishable state for arbitrary correlated internal states, while the fixed Fourier-interferometer protocol provides bounds for separable sources.

The authors explicitly identify extending the framework to higher mode occupations and continuous-variable photonic states, such as those used in Gaussian boson sampling, as an unresolved problem. Such an extension would broaden the applicability of the certification methods beyond the collision-free, fixed-photon-number setting analyzed in the paper.

References

Several practical and theoretical questions remain open. First, our analysis assumes lossless propagation and ideal photon-number-resolving detection; incorporating non-unit efficiencies and dark counts is important for applications to large photonic processors. Second, extending the framework beyond collision-free inputs to higher mode occupations, and to continuous-variable states such as those used in Gaussian boson sampling , remains open.

— Optimal interferometric certification of multi-photon indistinguishability  (2609.37620 - Robbio et al., 29 Sep 2026) in Section Conclusion