License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2017.20
URN: urn:nbn:de:0030-drops-80389
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8038/
Go to the corresponding LIPIcs Volume Portal


Reutter, David ; Vicary, Jamie

A 2-Categorical Approach to Composing Quantum Structures

pdf-format:
LIPIcs-CALCO-2017-20.pdf (0.6 MB)


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.

BibTeX - Entry

@InProceedings{reutter_et_al:LIPIcs:2017:8038,
  author =	{David Reutter and Jamie Vicary},
  title =	{{A 2-Categorical Approach to Composing Quantum Structures}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{20:1--20:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Filippo Bonchi and Barbara K{\"o}nig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8038},
  URN =		{urn:nbn:de:0030-drops-80389},
  doi =		{10.4230/LIPIcs.CALCO.2017.20},
  annote =	{Keywords: quantum constructions, 2-category, graphical calculus, planar algebra}
}

Keywords: quantum constructions, 2-category, graphical calculus, planar algebra
Collection: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Issue Date: 2017
Date of publication: 17.11.2017


DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI