Bell state entanglement swappings over collective noises and their applications on quantum cryptography

This work presents two robust entanglement swappings against two types of collective noises, respectively. The entanglement swapping can be achieved by performing two Bell state measurements on two logical qubits that come from two original logical Bell states, respectively. Two fault tolerant quantum secret sharing (QSS) protocols are further proposed to demonstrate the usefulness of the newly proposed entanglement swappings. The proposed QSS schemes are not only free from Trojan horse attacks but also quite efficient. Moreover, by adopting two Bell state measurements instead of four-qubit joint measurements, the proposed protocols are practical in combating collective noises. The proposed fault tolerant entanglement swapping can also be used to replace the traditional Bell-state entanglement swapping used in various quantum cryptographic protocols to provide robustness in combating collective noises.