Security proof for quantum cryptography against entanglement-measurement attack

Entanglement-measurement attack is one of the most famous attacks against quantum cryptography. In quantum cryptography protocols, eavesdropping checking is an effective means to resist this attack. There are currently two commonly used eavesdropping checking methods: one is to prepare two sets of non-orthogonal single-particle states as decoy states, and determine whether there are eavesdroppers in the quantum channel by comparing the states obtained by measurements with the original states; The other is to prepare two sets of non-orthogonal entangled states and use their entanglement correlations to judge whether there are eavesdroppers in the quantum channel. In this paper, we theoretically demonstrate how quantum cryptography can utilize these two eavesdropping checking methods to resist entanglement-measurement attacks. We take the quantum cryptography protocols based on maximally entangled states as examples to demonstrate the proof process, transitioning from qubit-based protocols to qudit-based ones.