A digital signature is a mathematical scheme for demonstrating the authenticity of a digital message or document. For signing quantum messages, some arbitrated quantum signature (AQS) schemes have been proposed. It was claimed that these AQS schemes could guarantee unconditional security. However, we show that they can be repudiated by the receiver Bob. To conquer this shortcoming, we construct an AQS scheme using a public board. The AQS scheme not only avoids being disavowed by the receiver but also preserves all merits in the existing schemes. Furthermore, we discover that entanglement is not necessary while all these existing AQS schemes depend on entanglement. Therefore, we present another AQS scheme without utilizing entangled states in the signing phase and the verifying phase. This scheme has three advantages: it does not utilize entangled states and it preserves all merits in the existing schemes; the signature can avoid being disavowed by the receiver; and it provides a higher efficiency in transmission and reduces the complexity of implementation.

In the existing semiquantum key distribution (SQKD) protocols, the both parties must measure qubits in some bases. In this paper, we show that the classical party’s measurement capability is not necessary by constructing an SQKD protocol without invoking the classical Alice’s measurement capability. In particular, we prove that the proposed SQKD protocol is completely robust against joint attacks. Compared with the existing SQKD protocols, the number of the quantum states sent by Alice and Bob is decreased.

In the preceding Comment [Phys. Rev. A 83, 046301 (2011)], Boyer and Mor pointed out that the first conclusion of Lemma 1 in our paper [X. Zou, D. Qiu, L. Li, L. Wu, and L. Li, Phys. Rev. A 79, 052312 (2009)] is not correct, and therefore, the proof of Theorem 5 based on Lemma 1 is wrong. Furthermore, they gave a direct proof for Theorem 5 and affirmed the conclusions in our original paper. In this Reply, we admit the first conclusion of Lemma 1 is not correct, but we need to point out that the second conclusion of Lemma 1 is correct. Accordingly, all the proofs for Lemma 2, Lemma 3, and Theorems 3\char21{}6 are based only on the second conclusion of Lemma 1 and therefore are correct.

Quantum entanglement is a fundamental physical resource that enables a range of information-processing tasks with no efficient solution on classical computers. In this paper, we construct a class of general maximum entangled states by parameterizing the coefficients of Bell states. By calculating, we obtain the local unitary operations required to realize the mutual transformation of the constructed states, analogous to Pauli operators acting on one particle of a Bell state. Interestingly, the local unitary operations on the two particles of Bell states are identical, whereas for the constructed states, they must differ in certain cases. To explore the potential applications of these maximum entangled states and the obtained local unitary operations, we design a class of measurement-device-independent quantum secure direct communication protocols based on entanglement swapping. In the class of designed protocols, entanglement swapping is realized between a constructed maximum entangled state and a Bell state. We demonstrate that the class of designed protocols have no information leakage and can resist intercept-and-resend attacks, measure-resend attacks, and collective attacks. In addition, the unconditional security of the class of designed protocols is proved. We believe that the constructed maximum entangled states and the obtained local unitary operations may find applications in other quantum information-processing fields.