Quantum Visual Secret Sharing Based on Position Superposition

Abstract

Quantum visual secret sharing scheme combines the traditional visual secret sharing scheme with quantum properties to improve the security of secret information. However, all existing quantum visual secret sharing schemes encode a single pixel as a quantum superposition state. Each pixel requires n qubits for encoding. The number of qubits required grows proportionally to the number of pixels, which is unfavorable when the secret image is large. To reduce the number of qubits used, we propose a (n, n)-threshold quantum visual secret sharing scheme based on position superposition. In the secret sharing phase, the position and the encoded color corresponding to the position of the image are encoded as a quantum superposition state simultaneously. The whole secret image is encoded only once instead of encoding individual pixels. Only \(\varvec{2m+n}\) qubits are required for a secret image of size \(\varvec{2^m \times 2^m}\). Then, the qubits encoding the position and the color of the secret image are distributed to n participants. In the recovery phase, n participants work together to recover the secret image by a quantum XOR operation on the qubits encoding the color. Simulations have been carried out to verify the practical feasibility of this scheme. Our scheme reduces the number of qubits used in the secret sharing process compared to previous quantum visual secret sharing schemes. In addition, there is no need to design the codebook in advance and the secret image can be fully recovered.