A protective scheme of quantum dense coding and quantum teleportation of the X-type initial state is proposed in amplitude damping noisy channel with memory using weak measurement and measurement reversal. Compared with the noisy channel without memory, the memory factor improves both the capacity of quantum dense coding and the fidelity of the quantum teleportation to a certain extent for the given damping coefficient. Although the memory factor can inhibit decoherence in some degree, it cannot eliminate it completely. In order to further overcome the influence of the damping coefficient, the weak measurement protective scheme is proposed, which found that the capacity and the fidelity can be efficiently improved by adjusting weak measurement parameter. Another practical conclusion is that, among the three initial states, the weak measurement protective scheme has the best protective effect on the Bell-state in terms of the capacity and the fidelity. For the channel with no memory and full memory, the channel capacity of quantum dense coding reaches two and the fidelity of quantum teleportation reaches one for the bit system; the Bell system can recover the initial state completely with a certain probability. It can be seen that the entanglement of the system can be well protected by the weak measurement scheme, which provides a good support for the realization of quantum communication.

In this paper, we study circuit complexity in Proca theory with Nielsen’s approach and Fubini-Study (FS) metric approach. We place the fields on a lattice to gain a regularized theory, and obtain the ground state by adopting proper coordinates. We calculate complexities of the ground and the thermofield double (TFD) states with Nielsen’s approach—complexity of the TFD state is found to grow like a logarithmic function. We quantize the Proca fields and give the approximate ground state and the TFD state by applying unitary circuit operators to the associated reference states. The circuit lengths are calculated with a FS metric—the minimal lengths are given according to the associated geometric spaces. The complexity of the TFD state is found to grow linearly with time.

The low-lying energy structures of small planar aluminum clusters Al_n (n = 3–6, 8–10), hydrogenated small planar aluminum clusters Al_nH_m (n = 3–8, m = 1–2) and the lowest-energy structure of Al_nH_m (n = 6–10, m = 0–2) are determined by density functional theory (DFT) calculations. Many stable planar structures have been found; some are consistent with the reported ones, and some are new configurations. The preservation of planar cluster structures has been observed during the dissociative adsorption of H₂.Hydrogen is adsorbed at different positions on planar aluminum clusters. Dissociative adsorption configurations of the planar structure and lowest-energy structure experienced a decrease in hydrogen adsorption energy with an increase in cluster size. Among the clusters we calculated, Al₄H₁ and Al₄H₂ have the highest HOMO-LUMO gap, indicating that they may be more abundant than other clusters. The geometric structure and electronic properties of these clusters are also discussed.

Entanglement states serve as the central resource for a number of important applications in quantum information science, including quantum key distribution, quantum precision measurement, and quantum computing. In pursuit of more promising applications, efforts have been made to generate entangled states with more qubits. However, the efficient creation of a high-fidelity multiparticle entanglement remains an outstanding challenge due to the difficulty that increases exponentially with the number of particles. We design an interferometer that is capable of coupling the polarization and spatial paths of photons and prepare 2-D four-qubit GHZ entanglement states. Using quantum state tomography, entanglement witness, and the violation of Ardehali inequality against local realism, the properties of the prepared 2-D four-qubit entangled state are analyzed. The experimental results show that the prepared four-photon system is an entangled state with high fidelity.