Genuinely quantum solutions of the game Sudoku and their cardinality

نویسندگان

چکیده

We expand the quantum variant of popular game Sudoku by introducing notion cardinality a (SudoQ), equal to number distinct vectors appearing in pattern. Our considerations are focused on genuinely solutions, which solutions size $N^2$ that have greater than $N^2$, and therefore cannot be reduced classical counterparts unitary transformation. find complete parameterization $4 \times 4$ SudoQ establish this case admissible cardinalities 4, 6, 8 16. In particular, solution with maximal 16 is presented. Furthermore, parametrization enabled us prove recent conjecture Nechita Pillet for special dimension. general, we proved any $N$ it possible an $N^2 N^2$ $N^4$, prime related set mutually unbiased bases $N^2$. Such construction $N^4$ different yields $N^3$ orthogonal measurements.

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ژورنال

عنوان ژورنال: Physical Review A

سال: 2021

ISSN: ['1538-4446', '1050-2947', '1094-1622']

DOI: https://doi.org/10.1103/physreva.104.042423