Their example of a difficult certification problem is sorting a defined number of photons after they have gone through a defined arrangement of several optical elements. The arrangement provides each photon with a number of transmission paths - depending on whether the photon is reflected or transmitted by an optical element. The task is to predict the probability of photons leaving the arrangement at defined points, for a given positioning of the photons at the entrance to the arrangement.
With increasing size of the optical arrangement and increasing numbers of photons sent on their way, the number of possible paths and distributions of the photons at the end rises steeply as a result of the uncertainty principle which underlies quantum mechanics - so that there can be no prediction of the exact probability using the computers available to us today. Physical principles say that different types of particle - such as photons or electrons - should yield differing probability distributions. But how can scientists tell these distributions and differing optical arrangements apart when there is no way of making exact calculations?
An approach developed in Freiburg by researchers from Rome, Milan; Redmond, USA; Paris, and Freiburg now makes it possible for the first time to identify characteristic statistical signatures across unmeasurable probability distributions. Instead of a complete "fingerprint", they were able to distill the information from data sets which were reduced to make them usable. Using that information, they were able to discriminate various particle types and distinctive features of optical arrangements. The team also showed that this distillation process can be improved, drawing upon established techniques of machine learning, whereby physics provides the key information on which data set should be used to seek the relevant patterns. And because this approach becomes more accurate for bigger numbers of particles, the researchers hope that their findings take us a key step closer to solving the certification problem.
Taira Giordani, Fulvio Flamini, Matteo Pompili, Niko Viggianiello, Nicolò Spagnolo, Andrea Crespi, Roberto Osellame, Nathan Wiebe, Mattia Walschaers, Andreas Buchleitner and Fabio Sciarrino are the authors of the paper titled " Experimental statistical signature of many-body quantum interference ". It has been published inNature Photonics.