A 2-Categorical Approach to Composing Quantum Structures

David Reutter, Jamie Vicary, Marc Herbstritt
<span title="2017-11-02">2017</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6konswtstrh6lafosqaq62ytpe" style="color: black;">Conference on Algebra and Coalgebra in Computer Science</a> </i> &nbsp;
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
more &raquo; ... these techniques to construct a unitary error basis that cannot be built using any previously known method. Digital Object Identifier 10.4230/LIPIcs.CALCO.2017.20 * An extended version of this paper can be found at [44], https://arxiv.org/abs/1609.07775. 1 Formally this is a common generalization of the tensor [23, Example 2.6] and spin model [23, Example 2.8] planar algebras, corresponding to a fragment of the monoidal 2-category 2Hilb [4] . However, our exposition will be elementary, and we will not assume knowledge of these ideas.
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