Verifiable Hybrid Secret Sharing With Few Qubits

We consider the task of sharing a secret quantum state in a quantum network in a verifiable way. We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols. To achieve this, we combine classical encryption of the quantum secret with an existing verifiable quantum secret sharing scheme based on Calderbank-Shor-Steane quantum error correcting codes. In this way we obtain a verifiable hybrid secret sharing scheme for sharing a qubit, which combines the benefits of quantum and classical schemes. Our scheme attains maximum secrecy allowed by quantum mechanics. Moreover, each of the n nodes holds only single-qubit shares and requires workspace of at most 3n qubits at a time to verify the quantum secret. Furthermore, we define a ramp verifiable hybrid scheme. We give explicit examples of ramp schemes and schemes achieving maximum secrecy based on existing quantum error correcting codes. Finally, we prove that our protocol is secure in the presence of an active non-adaptive adversary.