  We study teleportation with identical massive particles. Indistinguishability
imposes that the relevant degrees of freedom to be teleported are not
particles, but rather addressable orthogonal modes. We discuss the performances
of teleportation under the constraint of conservation of the total number of
particles. The latter inevitably decreases the teleportation fidelity.
Moreover, even though a phase reference, given by the coupling to a reservoir,
circumverts the constraint, it does not restore perfect deterministic
teleportation. The latter is only achievable with some special resource
entangled states and when the number of particles tends to infinity.
Interestingly, some of such states are the many-particle atomic coherent states
and the ground state of cold atoms loaded into a double well potential, which
are routinely prepared in experiments.
