Recently, Yamaguchi and Kempf proved that encrypted qubits can be cloned. In this work we generalize the encrypted cloning protocol and prove that it also applies to higher-order quantum systems. Given that a straightforward generalization of the protocol using the exponential of the shift and phase operators fails to satisfy the unitary requirement for a quantum gate, we propose a different approach. We introduce an alternative operator to be used in the encryption process and show that it is unitary. We adapt the decryption operator from the reference paper to fit in the framework of multilevel quantum systems. We analyze the circuit implementation of the proposed operators and show that the encryption could be implemented with a gate complexity that is independent of qudit dimension.

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• Quantum circuits
• Quantum information processing
• Quantum information theory