problem, and may readily be generalized to $n$-photon states, and indeed, multiple channels of $n$-photon states. The quantum filter for the extended system is presented in Section \[sec:matrix-filter\], with a derivation extending the reference method appearing in Section \[sec:extended-filter\]. The filtering results for the extended system are used to find the filtering equations for the original problem involving a single photon field in Section \[sec:single-photon-filter\]. The superposition of coherent field states is defined in Section \[sec:cat-super\], and a suitable embedded system for this case is described in Section \[sec:cat-embed\]. The corresponding master and filtering equations are presented in Sections \[sec:cat-master\] and \[sec:cat-super-filter\], respectively. Some concluding remarks are made in Section \[sec:conclusion\].

In this paper we are not concerned with technical issues concerning domains of unbounded operators and related matters, and indeed, we assume that the system operators are bounded, and that all quantum stochastic integrals are well-defined in the sense of Hudson-Parthasarathy, [@HP84].

*Notation:* We use the standard Dirac notation $\vert \psi \rangle$ to denote state vectors (vectors in a Hilbert space) [@EM98], [@AFP09]. The superscript $^\ast$ indicates Hilbert space adjoint or complex conjugate. The inner product of state vectors $\vert \psi_1 \rangle $ and $\vert \psi_2 \rangle$ is denoted 