On quantum measurement formulated in finite quantum mechanics in terms of dagger-compact categories in terms of Frobenius algebras and the quantum reader monad:
Bob Coecke, Eric Oliver Paquette, POVMs and Naimark’s theorem without sums, Electronic Notes in Theoretical Computer Science 210 (2008) 15-31 [arXiv:quant-ph/0608072, doi:10.1016/j.entcs.2008.04.015]
Bob Coecke, Eric Paquette, Dusko Pavlovic, Classical and quantum structures (2008) [pdf, pdf]
On quantum information theory via dagger-compact categories:
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