Verifiable Hybrid Secret Sharing With Few Qubits

TL;DR

This paper introduces a verifiable hybrid quantum secret sharing protocol that reduces qubit requirements by combining classical encryption with quantum error correction, enabling efficient and secure quantum state sharing.

Contribution

It presents a novel hybrid scheme that minimizes qubit usage per share and combines classical and quantum methods for verifiable quantum secret sharing.

Findings

Shares encoded in single qubits, reducing qubit requirements.

No information leakage to groups smaller than half the nodes.

Explicit examples based on existing quantum error correcting codes.

Abstract

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 qubits, which combines the benefits of quantum and classical schemes. Our scheme does not reveal any information to any group of less than half of the $n$ nodes participating in the protocol. Moreover, for sharing a one-qubit state each node needs a quantum memory to store $n$ single-qubit shares, and requires a workspace of at most $3n$ qubits in total to verify the quantum secret. Importantly, in our scheme an individual share is encoded in a single qubit, as opposed to previous schemes requiring $\Omega(\log n)$ qubits per share. Furthermore, we define a ramp verifiable hybrid scheme. We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes.