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

Abstract

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.

Figures (2)

• Figure 1: Quantum interferometric setup where $n$ single photons enter the first $n$ spatial modes of an $m$-mode linear interferometer $U$. The photon entering the $i$th mode carries specific internal degrees of freedom, represented by the internal state $\left| {\phi_i}\right\rangle$. The multimode bunching probability $P_{\kappa}$ corresponds to the probability that all $n$ photons are detected in the subset $\kappa$ of output modes (indicated by green detectors).
• Figure 2: Violation ratio $R$ (solid line) as defined in Eq. \ref{['eq:violation_ratio']}, quantifying the relative enhancement of the bunching probability as a function of the perturbation strength of the delay $d$. The perturbative approximation to second order $d^2$ is also plotted for comparison (dashed line). We observe that $R(d)$ exceeds $1$ in the neighborhood of indistinguishable particles, implying anomalous bunching.