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<jats:p>We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image. The core idea of this scheme is to embed information into object and background of cover image in different ways. First, a threshold method adopting the quantum informational entropy is employed to determine a threshold value. The threshold value can then be further used for segmenting the cover image to a binary image, which is an authentication key for embedding and extraction information. By a careful analysis of the quantum circuits of the scheme, that is, translating into the basic gate sequences which show the low complexity of the scheme. One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image. Furthermore, the analyses of peak signal-to-noise ratio, histogram and capacity of the scheme are also provided.</jats:p>

<jats:p>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 of participants. In the process of comparison, the 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 participants’ attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, but 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 the swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.</jats:p>

<jats:p>We propose a novel scheme for remote state preparation of an arbitrary three-qubit state with unit success probability, utilizing a nine-qubit cluster-GHZ state without introducing auxiliary qubits. Furthermore, we proceed to investigate the effects of different quantum noises (e.g., amplitude-damping, phase-damping, bit-flip and phase-flip noises) on the systems. The fidelity results of three-qubit target state are presented, which are usually used to illustrate how close the output state is to the target state. To compare the different effects between the four common types of quantum noises, the fidelities under one specific identical target state are also calculated and discussed. It is found that the fidelity of the phase-flip noisy channel drops the fastest through the four types of noisy channels, while the fidelity is found to always maintain at 1 in bit-flip noisy channel.</jats:p>

<jats:p>Fault-tolerant error-correction (FTEC) circuit is the foundation for achieving reliable quantum computation and remote communication. However, designing a fault-tolerant error correction scheme with a solid error-correction ability and low overhead remains a significant challenge. In this paper, a low-overhead fault-tolerant error correction scheme is proposed for quantum communication systems. Firstly, syndrome ancillas are prepared into Bell states to detect errors caused by channel noise. We propose a detection approach that reduces the propagation path of quantum gate fault and reduces the circuit depth by splitting the stabilizer generator into <jats:italic>X</jats:italic>-type and <jats:italic>Z</jats:italic>-type. Additionally, a syndrome extraction circuit is equipped with two flag qubits to detect quantum gate faults, which may also introduce errors into the code block during the error detection process. Finally, analytical results are provided to demonstrate the fault-tolerant performance of the proposed FTEC scheme with the lower overhead of the ancillary qubits and circuit depth.</jats:p>

<jats:p>Weinvestigate the vortex structures excited by Ioffe–Pritchard magnetic field and Dresselhaus-type spin–orbit coupling in <jats:italic>F</jats:italic> = 2 ferromagnetic Bose–Einstein condensates. In the weakly interatomic interacting regime, an external magnetic field can generate a polar-core vortex in which the canonical particle current is zero. With the combined effect of spin–orbit coupling and magnetic field, the ground state experiences a transition from polar-core vortex to Mermin–Ho vortex, in which the canonical particle current is anticlockwise. For fixed spin–orbit coupling strengths, the evolution of phase winding, magnetization, and degree of phase separation with magnetic field are studied. Additionally, with further increasing spin–orbit coupling strength, the condensate exhibits symmetrical density domains separated by radial vortex arrays. Our work paves the way to explore exotic topological excitations in high-spin systems.</jats:p>

<jats:p>We study the dynamics of geometric quantum discord (GQD) between two qubits, each qubit interacting at the same time with <jats:italic>K</jats:italic> independent multiple bosonic reservoirs at zero temperature. In both weak and strong qubit–reservoirs coupling regimes, we find that the increase of the number <jats:italic>K</jats:italic> of reservoirs can induce the damped oscillation of GQD, and enhance the memory effects of the overall environment. And the Hilbert–Schmidt norm GQD (two-norm GQD) is always smaller than the trace norm geometric quantum discord (one-norm GQD). Therefore, the one-norm GQD is a better way to measure the quantum correlation. Finally, we propose an effective strategy to improve GQD by using partially collapsing measurements, and we find that the protection effect is better with the increase of the weak measurement strength.</jats:p>

<jats:p>We report a metrology scheme which measures the magnetic susceptibility of an atomic spin ensemble along the <jats:italic>x</jats:italic> and <jats:italic>z</jats:italic> directions and produces parameter estimation with precision beating the standard quantum limit. The atomic ensemble is initialized via one-axis spin squeezing with optimized squeezing time and parameter <jats:italic>ϕ</jats:italic> (to be estimated) assumed as uniformly distributed between 0 and 2<jats:italic>π</jats:italic> while fixed in each estimation. One estimation of <jats:italic>ϕ</jats:italic> can be produced with every two magnetic susceptibility data measured along the two axes respectively, which has an imprecision scaling (1.43 ± 0.02)/<jats:italic>N</jats:italic> <jats:sup>0.687±0.003</jats:sup> with respect to the number <jats:italic>N</jats:italic> of the atomic spins. The measurement scheme is easy to implement and is robust against the measurement fluctuation caused by environment noise and measurement defects.</jats:p>

<jats:p>An image encryption algorithm is proposed in this paper based on a new four-dimensional hyperchaotic system, a neural mechanism, a Galois field and an improved Feistel block structure, which improves the efficiency and enhances the security of the encryption algorithm. Firstly, a four-dimensional hyperchaotic system with a large key space and chaotic dynamics performance is proposed and combined with a cloud model, in which a more complex and random sequence is constructed as the key stream, and the problem of chaotic periodicity is solved. Then, the key stream is combined with the neural mechanism, Galois field and improved Feistel block structure to scramble and diffuse the image encryption. Finally, the experimental results and security analysis show that the encryption algorithm has a good encryption effect and high encryption efficiency, is secure, and can meet the requirements of practical applications.</jats:p>

<jats:p>Accurate prediction of road traffic flow is a significant part in the intelligent transportation systems. Accurate prediction can alleviate traffic congestion, and reduce environmental pollution. For the management department, it can make effective use of road resources. For individuals, it can help people plan their own travel paths, avoid congestion, and save time. Owing to complex factors on the road, such as damage to the detector and disturbances from environment, the measured traffic volume can contain noise. Reducing the influence of noise on traffic flow prediction is a piece of very important work. Therefore, in this paper we propose a combination algorithm of denoising and BILSTM to effectively improve the performance of traffic flow prediction. At the same time, three denoising algorithms are compared to find the best combination mode. In this paper, the wavelet (WL) denoising scheme, the empirical mode decomposition (EMD) denoising scheme, and the ensemble empirical mode decomposition (EEMD) denoising scheme are all introduced to suppress outliers in traffic flow data. In addition, we combine the denoising schemes with bidirectional long short-term memory (BILSTM) network to predict the traffic flow. The data in this paper are cited from performance measurement system (PeMS). We choose three kinds of road data (mainline, off ramp, on ramp) to predict traffic flow. The results for mainline show that data denoising can improve prediction accuracy. Moreover, prediction accuracy of BILSTM+EEMD scheme is the highest in the three methods (BILSTM+WL, BILSTM+EMD, BILSTM+EEMD). The results for off ramp and on ramp show the same performance as the results for mainline. It is indicated that this model is suitable for different road sections and long-term prediction.</jats:p>

<jats:p>Investigating the thermal transport properties of materials is of great importance in the field of earth science and for the development of materials under extremely high temperatures and pressures. However, it is an enormous challenge to characterize the thermal and physical properties of materials using the diamond anvil cell (DAC) platform. In the present study, a steady-state method is used with a DAC and a combination of thermocouple temperature measurement and numerical analysis is performed to calculate the thermal conductivity of the material. To this end, temperature distributions in the DAC under high pressure are analyzed. We propose a three-dimensional radiative–conductive coupled heat transfer model to simulate the temperature field in the main components of the DAC and calculate <jats:italic>in situ</jats:italic> thermal conductivity under high-temperature and high-pressure conditions. The proposed model is based on the finite volume method. The obtained results show that heat radiation has a great impact on the temperature field of the DAC, so that ignoring the radiation effect leads to large errors in calculating the heat transport properties of materials. Furthermore, the feasibility of studying the thermal conductivity of different materials is discussed through a numerical model combined with locally measured temperature in the DAC. This article is expected to become a reference for accurate measurement of <jats:italic>in situ</jats:italic> thermal conductivity in DACs at high-temperature and high-pressure conditions.</jats:p>