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We study the non-Markovian dynamics of a qubit system coupled respectively to coherent state, squeezing vacuum state, and mixed state environments through dephasing interaction. Special attention is paid to the problem of environmental coherence and excitation on the effect of non-Markovianity of system dynamics. Some nontrivial and unexpected results are found. The number of environmental excitations serves to enhance the non-Markovianity of system dynamics, but the enhancement slows down with the increasing of the variance of excitation number. However, environmental coherence can play dual effects, which enhances in some cases and suppresses in other cases the non-Markovianity of system dynamics.

In this paper, by using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any participants. In the process of comparison, TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participant attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, and it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.

As one of the most important branches of quantum cryptography, quantum secure direct communication (QSDC) is used to transmit the secret message directly rather than distribute a random key. Quantum homomorphic encryption (QHE) enables arbitrary quantum transformation on encrypted data without decrypting the data. To date, the previously proposed QSDC schemes are mainly based on different quantum states. The research of the QSDC scheme based on QHE is still blank. In this paper, a QSDC scheme by taking advantage of the properties of QHE is proposed. The proposed protocol has applied QHE and decoy photons to prevent various types of attacks. The proposed scheme only utilizes the rotation operation to encode the secret message which is easy to implement with the current technologies. Moreover, the communication efficiency and the qubit-utilization ratio are analyzed in this paper, which shows that this protocol has good performance in the qubit-utilization ratio, and the qubit efficiency of the QSDC scheme has improved.