A 2-Categorical Approach to Composing Quantum Structures

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Authors

Colleges, School and Institutes

External organisations

  • University of Oxford

Abstract

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.

Details

Original languageEnglish
Title of host publication7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
EditorsFilippo Bonchi , Barbara König
Publication statusPublished - 2 Nov 2017
Event7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) - Ljubljana, Slovenia
Duration: 13 Jun 201716 Jun 2017

Publication series

NameLeibniz International Proceedings in Informatics (LIPIcs)
PublisherSchloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Volume72
ISSN (Electronic)1868-8969

Conference

Conference7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
CountrySlovenia
CityLjubljana
Period13/06/1716/06/17

Keywords

  • quantum constructions, 2-category, graphical calculus, planar algebra