2016/08/16 by Benjamin Musto, Musto, Benjamin · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #graph theory and CDMA systems #quant-ph
paper · pdf · doi:10.48550/arxiv.1608.04608
Submitted as thesis for MSc mathematics and the foundations of computer science, University of Oxford 2014
arxiv created 2016/08/16 · arxiv updated 2016/08/17
Unitary error bases have a great number of applications across quantum information and quantum computation, and are fundamentally linked to quantum teleportation, dense coding and quantum error correction. Werner's combinatorial construction builds a unitary error basis from a family of Hadamard matrices and a Latin square. In this dissertation, I give a new categorical axiomatisation of Latin squares, and use this to give a fully graphical presentation and proof of the correctness of Werner's construction. The categorical approach makes clear that some of the Latin square axioms are unnecessary for the construction to go through, and I propose a generalised construction scheme with the potential to create new classes of unitary error bases.