(G,G')-invariant quantum Latin squares are classified by trace- and conjugate-transpose-preserving isomorphisms of group algebras, and exist exactly when the groups have matching irreducible-representation degrees.
Algebraic graph theory , volume 207
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Group Invariant Quantum Latin Squares
(G,G')-invariant quantum Latin squares are classified by trace- and conjugate-transpose-preserving isomorphisms of group algebras, and exist exactly when the groups have matching irreducible-representation degrees.