Testing randomness with photons by direct characterization of optical t -designs

Generating and characterizing randomness is fundamentally important in both classical and quantum information science. Here we report the experimental demonstration of ensembles of pseudorandom optical processes comprising what are known as t-designs. We show that in practical scenarios, certain finite ensembles of two-mode transformations - 1- and 2-designs - are indistinguishable from truly random operations for 1- and 2-photon quantum interference, but they fail to mimic randomness for 2- and 3-photon cases, respectively. We make use of the fact that t-photon behavior is governed by degree-2t polynomials (in the parameters of the optical process), to experimentally verify the ensembles' behavior for complete bases of polynomials, ensuring that average outputs will be uniform for arbitrary configurations. It is in this sense that a t-design is deemed to be a potentially useful pseudorandom resource.