Entanglement between total intensity and polarization for pairs of coherent states

We examine entanglement between number and polarization, or between number and relative phase, for pairs of coherent states and two-mode squeezed vacuum via linear entropy and covariance criteria. We consider the embedding of the two-mode Hilbert space in a larger space to get a well-defined factorization of the number-phase variables. This can be regarded as a kind of proto-entanglement that can be extracted and converted into real particle entanglement via feasible experimental procedures. In particular this reveals interesting entanglement properties of pairs of coherent states.