POVMs and Naimark's Theorem Without Sums

duce an abstract notion of POVM within the categorical quantum mechanical semantics in terms act categories. Our definition is justified by two facts: i. we provide a purely graphical abstract counterpart to Naimark's theorem, which establishes a bijective correspondence between POVMs and abstract projective measurements on an extended system; ii. in the category of Hilbert spaces and linear maps our definition coincides with the usual one.

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Bob Coecke, Éric Oliver Paquette
• Keywords: Abstract Notion, ENTCS 2008, Graphical Abstract Counterpart, Quantum Mechanical Semantics