Robust Multi-Party Semi-Quantum Private Comparison Protocols with Decoherence-Free States against Collective Noises

Based on the decoherence-free states, two multi-party semi-quantum private comparison protocols are proposed to counteract collective noises. One can resist the collective-dephasing noise well, and the other can resist the collective-rotation noise. With the assistance of a semi-honest third party (TP), multiple classical participants with restricted quantum abilities can compare their secret information by performing the proposed protocols once. It is manifested that the proposed protocols can resist both external attacks and internal attacks. Additionally, the operations in the multi-party semi-quantum private comparison protocols are simulated on the IBM Quantum Experience.