Limits of multimode bunching for boson sampling validation: anomalous bunching induced by time delays

The multimode bunching probability is expected to provide a useful criterion for validating boson sampling experiments. Its applicability, however, is challenged by the existence of anomalous bunching, namely paradoxical situations in which partially distinguishable particles exhibit a higher bunching probability in two or more modes than perfectly indistinguishable ones. Using multimode bunching as a reliable criterion of genuine indistinguishability, therefore, requires a clear identification of the interferometric configurations in which anomalous bunching can or cannot occur. In particular, since uncontrolled small time delays between single-photon pulses constitute a common source of mode mismatch in current photonic platforms, it is essential to determine whether the resulting photon distinguishability might lead to anomalous bunching. Here, we first identify a broad class of interferometric configurations in which anomalous bunching is rigorously excluded, thereby establishing regimes where multimode bunching-based validation remains valid. Then, we find that, quite unexpectedly, temporal mode mismatch does not belong to this class. We exhibit a specific interferometric setup in which temporal distinguishability enhances multimode bunching, demonstrating that time delays can induce an anomalous behavior. These results help clarify the conditions under which multimode bunching remains a reliable validation tool.

💡 Research Summary

The paper investigates the reliability of using multimode bunching probabilities as a validation tool for boson‑sampling experiments, focusing on the phenomenon of “anomalous bunching” where partially distinguishable photons can produce a higher bunching probability than perfectly indistinguishable photons. The authors first formalize multimode bunching: for n photons entering an m‑mode linear interferometer U, the probability that all photons are detected within a chosen subset κ of output modes is Pκ = perm(H ⊙ S). Here H is a positive‑semidefinite Hermitian matrix determined solely by U and κ, while S is the Gram (distinguishability) matrix whose entries are the pairwise overlaps of the photons’ internal states (polarization, temporal mode, frequency, etc.). When photons are fully indistinguishable, S reduces to the all‑ones matrix E, giving Pκ = perm(H). The intuitive conjecture (P1) – that perm(H ⊙ S) ≤ perm(H) for any S – would guarantee that the maximal multimode bunching probability is achieved only for perfectly indistinguishable photons, making Pκ a universal indistinguishability witness.

However, earlier work showed that the Bapat‑Sunder permanent inequality, which underlies P1, is false in general; a 7‑photon counterexample was constructed, and Ref.