Large sets of mutually orthogonal quantum Latin squares
arXiv:2607.12933
summary
The paper studies the maximum size of sets of mutually orthogonal quantum Latin squares, proving that any set of n‑2 such squares of order n must be classical and constructing larger non‑classical sets for prime‑power orders, which improves existing 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.
Correction of Theorem 6
Topics & keywords
#mutually orthogonal quantum latin squares#combinatorial designs#quantum combinatorics#latin squares#prime power ordersMOQLSclassical vs non‑classicalorthogonal latin squaresboundsprime power