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This paper advances the theoretical boundaries of quantum information theory by constructing large sets of mutually orthogonal quantum Latin squares (MOQLS) with improved bounds for prime power orders. The research clarifies structural limitations, proving that any set containing n-2 such squares must be classical while demonstrating significant potential in non-classical configurations. These mathematical refinements are fundamental to optimizing protocols in quantum communication and error correction schemes reliant on orthogonal array structures.

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Large sets of mutually orthogonal quantum Latin squares

arXiv28 iulie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2607.12933v2 Announce Type: replace-cross Abstract: How large can a set of mutually orthogonal quantum Latin squares (MOQLS) get? We show that a set of n - 2 MOQLS of order n is necessarily classical and construct large non-classical sets of MOQLS of orders that are prime powers, improving both the previously known lower and upper bounds.

Abstract:How large can a set of mutually orthogonal quantum Latin squares (MOQLS) get? We show that a set of n - 2 MOQLS of order n is necessarily classical and construct large non-classical sets of MOQLS of orders that are prime powers, improving both the previously known lower and upper bounds.

Combinatorics (math.CO); Quantum Physics (quant-ph)

arXiv:2607.12933 [math.CO]

(or arXiv:2607.12933v2 [math.CO] for this version)

https://doi.org/10.48550/arXiv.2607.12933 Focus to learn more arXiv-issued DOI via DataCite

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