  In this paper, we investigate the dynamics of quantum linear systems where
the input signals are multi-channel multi-photon states, namely states
determined by a definite number of photons superposed in multiple input
channels. In contrast to most existing studies on separable input states in the
literature, we allow the existence of quantum correlation (for example quantum
entanglement) in these multi-channel multi-photon input states. Due to the
prevalence of quantum correlations in the quantum regime, the results presented
in this paper are very general. Moreover, the multi-channel multi-photon states
studied here are reasonably mathematically tractable. Three types of
multi-photon states are considered: 1) $m$ photons superposed among $m$
channels, 2) $N$ photons superposed among $m$ channels where $N\geq m$, and 3)
$N$ photons superposed among $m$ channels where $N$ is an arbitrary positive
integer. Formulae for intensities and states of output fields are derived.
Examples are used to demonstrate the effectiveness of the results.

Quantum Physics