1. Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, I-00185 Roma, Italy;
2. Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (IFN-CNR), Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy;
3. Dipartimento di Fisica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, I-20133 Milano, Italy;
4. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON N2L 2Y5, Canada;
5. Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Niterói, RJ 24210-340, Brazil
Corresponding author (email:
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single- and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.
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