The purpose of this paper is to present general algebraic methods for describing quantum networks. These methods are motivated by new imperatives of quantum network analysis and design, in particular, feedback control. The basic tools in our methodology are a matrix representation of open quantum systems, and the concatenation and series products of two such systems. We show how these methods can be used to efficiently model open quantum systems, or networks of such systems.We also explain how quantum feedback networks can be designed using these methods.

© 2007 Optical Society of America

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