Robust Estimators of Genuine Multiparticle Indistinguishability

The dynamics of noninteracting bosons has attracted interest due to the BosonSampling problem and its computational difficulty. A challenge in experimental systems implementing these dynamics is verifying that the output distributions are close to the desired ones. Motivated by a cold atom optical lattice experiment, we formalize the notion of genuine multiparticle indistinguishability, making use of tools from representation theory. We then construct novel witnesses of it, aiming for small variance and robustness to small miscalibrations of the unitary that governs the dynamics. We also discuss the possibility of using the representation theoretic framework to infer the linear optical unitary, by preparing many initial states.