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.

Comment: 26 pages, many pics; this third version has substantially more explanations than previous ones; Journal reference is of short 14 page version; Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL), Lecture Notes in Computer Science 6247, Springer-Verlag (2010)

• 68Q12 - Quantum algorithms and complexity in the theory of computing
• 81P45 - Quantum information, communication, networks (quantum-theoretic aspects)
• 81P68 - Quantum computation
• 81P70 - Quantum coding (general)