Environment and classical channels in categorical quantum mechanics

TL;DR

This paper introduces a graphical calculus for quantum computing that axiomatizes environments and classical channels, enabling structured reasoning about quantum protocols and classical control within a unified framework.

Contribution

It provides a simple, comprehensive graphical framework that axiomatizes environments and classical channels, enhancing the formal understanding of quantum protocols.

Findings

Axiomatization of environments and classical channels in graphical calculus

Enables constructive representation of quantum protocols

Derives correctness of quantum informatic protocols

Abstract

We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the earlier introduced axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.