Robust multi-party semi-quantum private comparison protocols with decoherence-free states against collective noises

Based on decoherence-free states, two multi-party semi-quantum private comparison protocols are proposed to counteract collective noises. One could resist the collective-dephasing noise well, whereas the other could resist the collective-rotation noise. Multiple classical participants could compare their secret information by performing the proposed protocols once. It is manifested that the proposed protocols could resist both external attacks and internal attacks. Besides, the operations of our protocols were simulated on the IBM Quantum Experience.