Ruling out the class of statistical processes involving two noninteracting identical particles in two modes

In the framework of generalized probabilistic theories (GPT), we illustrate a class of statistical processes in the case of two noninteracting identical particles in two modes that satisfies a well-motivated notion of physicality conditions, namely the double stochasticity and the no-interaction condition proposed by Karczewski [Phys. Rev. Lett. 120, 080401 (2018)]10.1103/PhysRevLett.120.080401, which cannot be realized through a quantum mechanical process. This class of statistical process is ruled out by an additional requirement, called the evolution condition, imposed on two-particle evolution. We also show that any statistical process of two noninteracting identical particles in two modes that satisfies all three physicality conditions can be realized within quantum mechanics using the beam-splitter operation.