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

• URL: http://arxiv.org/abs/2206.03599v2
• Date: Fri, 25 Nov 2022 08:55:28 GMT
• Title: Multi-qubit doilies: enumeration for all ranks and classification for ranks four and five
• Authors: Axel Muller, Metod Saniga, Alain Giorgetti, Henri De Boutray, Fr\'ed\'eric Holweck
• Abstract summary: For $N geq 2$, an $N$-qubit doily is a doily living in the $N$-qubit symplectic polar space. We present an effective algorithm for the generation of all $N$qubit doilies.
• Score: 0.20999222360659603
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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