  The purpose of this paper is to present a mathematical framework for
analyzing the response of quantum linear systems driven by multi-photon states.
Both the factorizable (namely, no correlation among the photons in the channel)
and unfactorizable multi-photon states are treated. Pulse information of
multi-photon input state is encoded in terms of tensor, and response of quantum
linear systems to multi-photon input states is characterized by tensor
operations. Analytic forms of output correlation functions and output states
are derived. The proposed framework is applicable no matter whether the
underlying quantum dynamic system is passive or active. The results presented
here generalize those in the single-photon setting studied in (Milburn, 2008)
and (Zhang and James, 2013}). Moreover, interesting multi-photon interference
phenomena studied in (Sanaka, Resch, and Zeilinger, 2006), (Ou, 2007), and
(Bartley, et al., 2012) can be reproduced in the proposed framework
