Three Quantum Latin Squares of Order 6 with Cardinalities 13, 15, and 17
Abstract
We give three explicit quantum Latin squares of order 6, with cardinalities 13, 15, and 17. Throughout, vectors differing only by a global phase are counted as identical. The cardinality-13 construction is based on an orthogonal direct-sum decomposition 6=42. The cardinality-15 and cardinality-17 constructions are based on two-dimensional Hadamard pairs supported on coordinate planes.
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