Fermion and boson beam-splitter statistics

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Abstract
Input-output relations are derived for a lossless beam splitter with two input arms and two output arms. The inputs are two-particle states, either fermions or bosons, with both particles in the same arm or one in each of the input arms. The output states are derived for the four distinct two-particle input states. The statistics of the outputs for fermion and boson inputs are compared with each other and with the statistics for classical particles. For input particles in the same arm, the output statistics are the same for all three varieties of particle. For input particles in different arms, the output particle-number variances are reduced for fermions but increased for bosons, while the interarm correlation is increased for fermions but reduced for bosons in comparison to classical particles.