Generalized suppression law for validation of Boson Sampling

Summary form only given. Recently, interference of multi-particle states has raised a strong interest in the scientific community, since it is believed to be at the very heart of post-classical computation. In this context, Boson Sampling [1] devices exploit multi-photon interference effects to provide evidence of a superior quantum computational power with current state-of-the-art technology. Thus, the capability to correctly certify the presence of multi-particle interference and find optimal platforms, becomes a crucial task because is expected to find numerous applications in photonic quantum information as a diagnostic tool for quantum optical devices.We investigate different scenarios, namely, when the consider only a fixed set of input modes, but also for the situation where all input sets can be used. We find that, in certain cases, the best choice for this task consist of Hadamard [2,3] interferometers which we implemented with a novel architecture enabled by the 3D capabilities of femtosecond laser writing. We derive and experimentally demonstrate a novel zero-transmission law based on symmetric interferometers (Fig. 1) and we verifyied the optimality of these platforms by performing further Bayesian analysis and by maximizing the total variation distance between the probability distributions corresponding to indistinguishable and distinguishable particles. The results suggest an immediate application for scattershot Boson Sampling experiments [4], where an exponential advantage in terms of generation rate is obtained with respect to the fixed-input problem. The main advantage of this technique consists in the large fraction of input-output suppressed combinations when these trasformations are injected with indistinguishable photons. In summary, this work represents a further step for quantum interference analysis and it is worth noting that Hadamard matrices naturally appear as the optimal designs for identifying genuine photonic indistinguishability in multimode interferometers and a powerful tool to validate Boson Sampling experiments. We aknowledge QUCHIP and 3D-Quest for funding this work.