Quantum Filtering for Systems Driven by Fields in Single Photon States and Superposition of Coherent States using Non-Markovian Embeddings

TL;DR

This paper develops quantum filtering and master equations for systems driven by non-classical fields, specifically single photon states and superpositions of coherent states, using non-Markovian embedding techniques.

Contribution

It introduces a novel approach to derive quantum filters for non-Markovian systems driven by complex quantum states, expanding the applicability of quantum stochastic calculus.

Findings

Derived coupled master equations for non-classical field states.

Formulated quantum filters using non-Markovian embeddings.

Provided a framework for continuous monitoring of quantum systems in complex states.

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.