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arXiv · 2206.03599

Multi-qubit doilies: enumeration for all ranks and classification for ranks four and five

Axel Muller·Metod Saniga·Alain Giorgetti·Henri De Boutray·Frédéric Holweck
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Abstract

For $N \geq 2$, an $N$-qubit doily is a doily living in the $N$-qubit symplectic polar space. These doilies are related to operator-based proofs of quantum contextuality. Following and extending the strategy of Saniga et al. (Mathematics 9 (2021) 2272) that focused exclusively on three-qubit doilies, we first bring forth several formulas giving the number of both linear and quadratic doilies for any $N > 2$. Then we present an effective algorithm for the generation of all $N$-qubit doilies. Using this algorithm for $N=4$ and $N=5$, we provide a classification of $N$-qubit doilies in terms of types of observables they feature and number of negative lines they are endowed with. We also list several distinguished findings about $N$-qubit doilies that are absent in the three-qubit case, point out a couple of specific features exhibited by linear doilies and outline some prospective extensions of our approach.

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Axel Muller, Metod Saniga, Alain Giorgetti, Henri De Boutray, Frédéric Holweck. 2022-06-07. Multi-qubit doilies: enumeration for all ranks and classification for ranks four and five. https://doi.org/10.1016/j.jocs.2022.101853

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