Starting from a fixed initial statesay, |I =|1,…,1,0,…0 you get to choose any m m mode-mixing unitary U U induces an unitary (U) on n-photon states, defined by Linear Optics for Dummies (or computer scientists) Computational basis states have the form |S =|s 1,…,s m, where s 1,…,s m are nonnegative integers such that s 1 +…+s m =n n = # of identical photons m = # of modes For us, m>n Then you get to measure (U)|I in the computational basis Here U S,T is an n n matrix obtained by taking s i copies of the i th row of U and t j copies of the j th column, for all i,j
{}