Partial indistinguishability theory for multiphoton experiments in multiport devices
V. S. Shchesnovich · Physical Review A · 2015
We generalize an approach for description of multiphoton experiments with multiport unitary linear optical devices, started in Phys. Rev. A 89, 022333 (2014) with single photons in mixed spectral states, to arbitrary (multiphoton) input and arbitrary photon detectors. We show that output probabilities are always given in terms of the matrix permanents of the Hadamard product of a matrix built from the network matrix and matrices built from the spectral state of photons and spectral sensitivities of detectors. Moreover, in the case of input with up to one photon per mode, the output probabilities are given by a sum (or integral) with each term being the absolute value squared of such a matrix permanent. We conjecture that, for an arbitrary multiphoton input, zero output probability of an output configuration is always the result of an exact cancellation of quantum transition amplitudes of completely indistinguishable photons (a subset of all input photons) and, moreover, is independent of coherence between only partially indistinguishable photons. The conjecture is supported by examples. Furthermore, we propose a measure of partial indistinguishability of photons which generalizes Mandel's observation, and find the law of degradation of quantum coherence in a realistic boson-sampling device with increase of the total number of photons and/or their ``classicality parameter.''