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math.CO2026
Large sets of mutually orthogonal quantum Latin squares
Simeon Ball, Robin Simoens
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-classica…
quant-ph2026
Mixed-dimensional quantum MacWilliams identity: Bounds for codes and absolutely maximally entangled states in heterogeneous systems
David González-Lociga, Simeon Ball
As emerging quantum architectures evolve into heterogeneous networks combining different physical substrates, such as qubits for logic and higher-dimensional qudits for robust comm…
quant-ph2026
Thirty-six quantum officers are entangled
Simeon Ball, Robin Simoens
There exist pairs of orthogonal Latin squares of any order n except if n=2 or n=6 [Bose, Shrikhande and Parker, 1960]. In particular, the problem of Euler's thirty-six officers doe…