Unauthorized subsets in qudit encrypted cloning are uninformative exactly when a congruence system has only the trivial solution, classified by a greatest-common-divisor condition that extends the qubit parity case.
Quantum error correction beyond su (2): spin, bosonic, and permutation-invariant codes from convex geometry.PRX Quantum, 7(1):010341
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Classification of informative subsets in quantum encrypted cloning on qudits
Unauthorized subsets in qudit encrypted cloning are uninformative exactly when a congruence system has only the trivial solution, classified by a greatest-common-divisor condition that extends the qubit parity case.