Biunitary constructions in quantum information

TL;DR

This paper introduces new construction schemes for quantum information structures using biunitary connections, expanding the toolkit for building unitary error bases and related objects with graphical calculus.

Contribution

It presents novel infinite construction schemes involving biunitary connections, many previously undescribed, and demonstrates a new unitary error basis not achievable by existing methods.

Findings

Developed new construction schemes for quantum structures

Introduced a graphical calculus for biunitary connections

Constructed a unique unitary error basis not obtainable by prior methods

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.