We introduce a new class of continuous matrix product (CMP) states and
establish the stochastic master equations (quantum filters) for an arbitrary
quantum system probed by a bosonic input field in this class of states. We show
that this class of CMP states arise naturally as outputs of a Markovian model,
and that input fields in these states lead to master and filtering (quantum
trajectory) equations which are matrix-valued. Furthermore, it is shown that
this class of continuous matrix product states include the (continuous-mode)
single photon and time-ordered multi-photon states.Comment: 17 pages, 2 figure
