# Partial distinguishability, permutation symmetry, and normal modes in multi photon coincidence

This seminar will cover recent work on the analysis of interferometry experiments using partially distinguishable photons. The analysis simplifies nicely using the permutation group and introducing a ``rate matrix’’. For a fixed measurement operator this rate matrix does not depend on the input distribution of photons; the rate matrix can be block-diagonalized using permutation group methods only. The ``normal coordinates’’ associated with this diagonalization have a simple interpretation in terms of unitary group functions and photon states of definite permutation symmetries and partial distinguishability. This holds (with some modifications) even when the number of photons per input is greater than one.

This work was done in collaboration with Barry Sanders, Abdullah Khalid, Dylan Spivak and others.