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Supplementarity is necessary for quantum diagram reasoning

Abstract:

The ZX-calculus is a powerful diagrammatic language for quantum mechanics and quantum information processing. We prove that itsπ4-fragment is not complete, in other words the ZXcalculus 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, itsπ2-fragme...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.4230/LIPIcs.MFCS.2016.76

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Computer Science
Role:
Author
Publisher:
Schloss Dagstuhl Publisher's website
Publication date:
2016-08-19
Acceptance date:
2016-06-05
DOI:
ISSN:
1868-8969
Pubs id:
pubs:683920
URN:
uri:a1cab443-74b1-48ab-a88a-66085a5b1ce5
UUID:
uuid:a1cab443-74b1-48ab-a88a-66085a5b1ce5
Local pid:
pubs:683920
ISBN:
9783959770163

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