Discrimination and decoherence of Schrödinger cat states in lossy quantum channels

We investigate environment induced effects of decoherence in discrimination between the Schrödinger cat states transmitted through noisy quantum channels such as optical fibers. We calculate the fidelity and the statistics of photocounts for both even and odd coherent states. The method that uses the beam splitter-like transformation acting in the enlarged Hilbert space to model the quantum channel is compared with the approach based on the Lindblad dynamics of one-mode bosonic systems.