Supplementarity is Necessary for Quantum Diagram Reasoning *

Simon Perdrix 1 Quanlong Wang 2, 1
1 CARTE - Theoretical adverse computations, and safety
Inria Nancy - Grand Est, LORIA - FM - Department of Formal Methods
Abstract : The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that its π 4-fragment is not complete, in other words the ZX-calculus is not complete for the so called "Clifford+T quantum mechanics". The completeness of this fragment was one of the main open problems in categorical quantum mechanics, a programme initiated by Abramsky and Coecke. The ZX-calculus was known to be incomplete for quantum mechanics. On the other hand, its π
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Simon Perdrix, Quanlong Wang. Supplementarity is Necessary for Quantum Diagram Reasoning *. 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016), Aug 2016, Krakow, Poland. pp.76:1--76:14, ⟨10.4230/LIPIcs.MFCS.2016.76⟩. ⟨hal-01361419⟩

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