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Entanglement-assisted quantum error-correcting codes (abbreviate to EAQECCs) expand the usual paradigm of quantum error correction by allowing two parties to make use of pre-shared entanglement. It is well-known that we can construct an EAQECC from arbitrary classical linear code. In this paper, we construct several classes of entanglement-assisted quantum MDS (EAQMDS) codes by utilizing generalized Reed-Solomon (GRS) codes. The main contribution of the paper is extend the code length of EAQMDS in the literature (Guo et al. 2019). Consequently, the results show that almost all of these EAQMDS codes are new in the sense that the parameters of these codes are not covered by the previously known ones. [ABSTRACT FROM AUTHOR]

In order to protect the privacy of query users and databases, a quantum private query protocol under noisy conditions is proposed and studied. It is a one-way quantum protocol that not only protects user privacy, but also prevents eavesdropping. And in the protocol initialization phase, the identity is verified by the quantum entanglement pair. Through key distribution, a user only knows a part of the key, and the accuracy of the original key needs to be considered. Channel noise directly affects the transmission result of quantum bits and reduces the transmission accuracy. In addition, the presence of eavesdropper Eve may also affect the transmission of qubits. The receiver corrects the error by using quantum error correction technology, thereby improving the efficiency of protocol communication. [ABSTRACT FROM AUTHOR]