Multiphoton states related via linear optics

Abstract

We investigate which pure states of n photons in d modes can be transformed into each other via passive linear optics, without postselection. In other words, we study the local unitary (LU) equivalence classes of symmetric many-qudit states. Writing our state as f†|Ω, with f† a homogeneous polynomial in the mode creation operators, we propose two sets of LU invariants: spectral invariants, which are the eigenvalues of the operator ff†, and moments, each given by the norm of the symmetric component of a tensor power of the initial state, which can be computed as vacuum expectation values of fk(f†)k. We provide a scheme for experimental measurement of the later, as related to the postselection probability of creating state f†k|Ωfrom k copies of f†|Ω. © 2014 American Physical Society.