  We present analytical compact solution for the density matrix and correlation
functions of two collective-macroscopic spins evolving via Ising-like
Hamiltonian in the presence of particle losses. The losses introduce non-local
phase noise which destroys highly entangled states arising in the evolution. On
the other hand, the states appearing at relatively short timescales, possessing
EPR-like entanglement will survive. Applying our solutions to the recently
proposed scheme to entangle two Bose-Einstein condensates, we estimate the
optimal number of atoms for EPR correlations.
