Amplification of Schrodinger-cat state: distinguishability and interference in phase space

Amplification and cloning of the Schrodinger-cat state (even coherent-state superposition) in the optical nondegenerate parametric amplifier are analy sed. In the long-time limit, distinguishability and interference in the mar ginal probability distributions of the Schrodinger-cat state cannot be pres erved simultaneously during amplification. The mutual ratio between disting uishability and interference can be controlled by the squeezed vacuum state injected in the idler mode. Thus only one of either quantum interference o f indistinguishable states or distinguished states without interference can be obtained on the output of the amplifier. The purity of the initial stat e in the signal mode disappears during the amplification for both cases, ev en if the interference is preserved. Thus the interference in the marginal probability distribution is connected with indistinguishability in the phas e space rather than with purity of the state. On the other hand, the noncla ssical oscillations in the photon-number distribution vanish simultaneously , as the state is more mixed, irrespective of the existence of the interfer ence.