2026-08-18T13:39:50Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8038 2024-03-06T10:39:39Z ddc:004 open_access

A 2-Categorical Approach to Composing Quantum Structures Reutter, David Vicary, Jamie quantum constructions 2-category graphical calculus planar algebra We present an infinite number of construction schemes for quantum structures, including unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on the type structure of biunitary connections, 2-categorical structures which play a central role in the theory of planar algebras. They have an attractive graphical calculus which allows simple correctness proofs for the constructions we present. We apply these techniques to construct a unitary error basis that cannot be built using any previously known method. Schloss Dagstuhl – Leibniz-Zentrum für Informatik David Reutter and Jamie Vicary 2017 Is Part Of LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2017.20 urn:nbn:de:0030-drops-80389 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.20 eng https://creativecommons.org/licenses/by/3.0/legalcode