  Generating and characterising 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. This provides a novel optical test of pseudo randomness. We make
use of the fact that t-photon behaviour is governed by degree-2t polynomials in
the parameters of the optical process to experimentally verify the ensembles'
behaviour for complete bases of polynomials. This ensures that outputs will be
uniform for arbitrary configurations, satisfying the strict definition of
pseudorandomness implicit in the mathematical definition.
