Dagger Compact Closed Categories and Completely Positive Maps: (Extended Abstract)

ly positive maps (extended abstract) Peter Selinger 1 Department of Mathematics and Statistics Dalhousie University, Halifax, Nova Scotia, Canada Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name “strongly compact closed categories”, as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch a proof of its completeness for equational reasoning. We give a general construction, the CPM construction, which associates to each dagger compact closed category its “category of completely positive maps”, and we show that the resulting category is again dagger compact closed. We apply these ideas to Abramsky and Coecke’s interpretation of quantum protocols, and to D’Hondt and Panangaden’s predicate transformer semantics. Key words: Categorical model, quantum computing, dagger categories, CPM construction.

• Type: Journal
• Year: 2007
• Where: ENTCS
• Authors: Peter Selinger
• Keywords: Canada Dagger Compact, Dagger Compact, ENTCS 2007, Positive Maps