Quantum teleportation with close-to-maximal entanglement from a beam splitter

We investigate theoretically quantum teleportation by means of the number-sum and phase-difference variables. We show that a unitary beam-splitter transformation turns two-mode Fock-states into close-to-maximally entangled states, in this case close approximations of the relative-phase eigenstates. These states could be created experimentally using on-demand single-photon sources, but also with any second-quantized bosonic system (e.g., trapped ions, Bose-Einstein condensates). We show that such 'quasi-EPR' states can yield near-unity fidelity for the teleportation of coherent states and of 'Schroedinger cat' states