Biunitary constructions in quantum information
Abstract
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary connections, algebraic objects 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.07775
 arXiv:
 arXiv:1609.07775
 Bibcode:
 2016arXiv160907775R
 Keywords:

 Quantum Physics;
 Mathematics  Category Theory;
 Mathematics  Quantum Algebra
 EPrint:
 48 pages, Mathematica notebook attached