Multi-qubit doilies: Enumeration for all ranks and classification for ranks four and five
Résumé
For N ≥ 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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