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Communication Dans Un Congrès Année : 2016

Supplementarity is Necessary for Quantum Diagram Reasoning *

Résumé

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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Dates et versions

hal-01361419 , version 1 (07-09-2016)

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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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