We propose the schemes of quantum secure direct communication based on a secret transmitting order of particles. In these protocols, the secret transmitting order of particles ensures the security of communication, and no secret messages are leaked even if the communication is interrupted for security. This strategy of security for communication is also generalized to a quantum dialogue. It not only ensures the unconditional security but also improves the efficiency of communication.

We propose several schemes for implementing a two-qubit quantum phase gate between two Rydberg atoms. The schemes could be realized in one step without adiabatic passage which depends on the specifical shapes and tailored pulse sequences of the laser fields. When the Rydberg-Rydberg-interaction (RRI) strength and the parameters of the driving fields satisfy some certain conditions, the effective Rabi oscillation between the two-excitation Rydberg state and the ground state would be generated, which is out of the Rydberg blockade regime and essential for our scheme. In addition, the individual addressing of the atoms is not required. And the schemes can work under strong or weak RRI strength. The imperfections induced by the variation of RRI strength and spontaneous emission are discussed through solving the master equation numerically.

We study the effects of parity-time ($\mathcal{PT}$) symmetry on the photon blockade and distinguish the different blockade mechanisms in a double-cavity optomechanical system. By studying the light statistics of the system, we find the completely different photon blockade behaviors when the $\mathcal{PT}$ symmetry is broken or unbroken, which is related to the $\mathcal{PT}$ phase transition. Furthermore, an interesting phenomenon that the two cavities are blocked at the same time is found with the appropriate system parameters. Those statistical phenomena are all analyzed in detail and demonstrated by analytically solving the Schrödinger equation and numerically simulating the master equation, respectively. Finally, we also consider the non-$\mathcal{PT}$-symmetric situations which further reveal the physical essence of the photon blockade by comparing those results. Different from the usual photon blockade, our proposal is feasible even with weak parameter mechanism, i.e., the proposal neither requires the strong optomechanical coupling nor the large tunneling coupling between cavities.

We propose a simplified parity meter for photonic qubits with cross-Kerr nonlinearities, homodyne measurement, and some optical elements. Our scheme has lower error probability than the protocol proposed in Nemoto and Munro [ Phys. Rev. Lett. 93, 250502 (2004)]. Based on the present parity meter, we achieve cluster-state preparation, a complete Bell-state analyzer, and quantum teleportation. All of these schemes are nearly deterministic in the regime with little noise and include less optical elements, which makes our schemes more meaningful for large-scale quantum computing.

Inspired by recent work [Carr and Saffman, Phys. Rev. Lett. 111, 033607 (2013)], we propose a simplified scheme to prepare the two-atom maximally entangled states via dissipative Rydberg pumping. Compared with the former scheme, the simplified one involves fewer classical laser fields and Rydberg interactions, and the asymmetric Rydberg interactions are avoided. Master equation simulations demonstrate that the fidelity and the Clauser-Horne-Shimony-Holt correlation of the maximally entangled state could reach up to 0.999 and 2.821, respectively, under certain conditions. Furthermore, we extend the physical thoughts to prepare the three-dimensional entangled state, and the numerical simulations show that, in theory, both the fidelity and the negativity of the desired entanglement could be very close to unity under certain conditions.