---
abstract: 'The purpose of this paper is to determine quantum master and filter equations for systems coupled to fields in certain non-classical continuous-mode states. Specifically, we consider two types of field states (i) single photon states, and (ii) superpositions of coherent states. The system and field are described using a quantum stochastic unitary model. Master equations are derived from this model and are given in terms of systems of coupled equations. The output field carries information about the system, and is continuously monitored. The quantum filters are determined with the aid of an embedding of the system into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.'
author:
- 'John E. Gough[^1]'
- 'Matthew R. James[^2]'
- 'Hendra I. Nurdin[^3]'
title: 'Quantum Filtering for Systems Driven by Fields in Single Photon States and Superposition of Coherent States using Non-Markovian Embeddings[^4]'
---

Keywords: quantum filtering, continuous-mode single photon states, continuous-mode superpositions of coherent states, quantum stochastic processes

Introduction
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In recent years single photon states of light and superpositions of coherent states have become increasingly important due to applications in quantum technology, in particular, quantum computing and quantum information systems, [@MHNWGBRH97], [@GM08], [@KLM01], [@GRTZ02], 