  The purpose of this paper is to derive filters for an arbitrary open quantum
system driven by a light wavepacket prepared in a continuous-mode multi-photon
state. A continuous-mode multi-photon state is a state of a travelling light
wavepacket that contains a definite number of photons and is characterised by a
temporal (or equivalently spectral) profile. After the interaction with the
system, the outgoing light can be monitored by means of homodyne detection or
photodetection. Filters for both measurement schemes are derived in this paper.
Unlike the vacuum or the coherent state case, the annihilation operator of the
light field acting on a multi-photon state changes the state by annihilating a
photon, and this makes the traditional filtering techniques inapplicable. To
circumvent this difficulty, we adopt a non-Markovian embedding technique
proposed in \cite{gough:2013} for the study of the single-photon filtering
problem. However, the multi-photon nature of the problem addressed in this
paper makes the study much more mathematically involved. Moreover, as
demonstrated by an example --- a two-level system driven by a continuous-mode
two-photon state, multi-photon filters can reveal interesting strong nonlinear
optical phenomena absent in both the single-photon state case and the
continuous-mode Fock state case.
