Quantum kk-uniform states from quantum orthogonal arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\geq 6$ and $N\neq 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\geq 7$ for arbitrary $N\geq 7$.Comment: 26 pages, 1 figure

Mutually unbiased maximally entangled bases from difference matrices

Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $\mathbb{C}^q\otimes \mathbb{C}^q$ for arbitrary prime power $q$. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in $\mathbb{C}^{12}\otimes \mathbb{C}^{12}$ and $\mathbb{C}^{21}\otimes\mathbb{C}^{21}$, which improve the known lower bounds for $d=3m$, with $(3,m)=1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we construct $p+1$ mutually unbiased bases with $p$ maximally entangled bases and one product basis in $\mathbb{C}^p\otimes \mathbb{C}^{p^2}$ for arbitrary prime number $p$.Comment: 24 page

A New Chaotic Image Encryption Algorithm Based on Transversals in a Latin Square

In this paper, a new combinatorial structure is introduced for image encryption, which has an excellent encryption effect on security and efficiency. An n-transversal in a Latin square has the function of classifying all the matrix’s positions, and it can provide a pair of orthogonal Latin squares. Employing an n-transversal of a Latin square, we can permutate all the pixels of an image group by group for the first time, then use two Latin squares for auxiliary diffusion based on a chaotic sequence, and finally, make use of a pair of orthogonal Latin squares to perform the second scrambling. The whole encryption process is “scrambling–diffusion–scrambling”. The experimental results indicated that this algorithm passed various tests and achieved a secure and fast encryption effect, which outperformed many of the latest papers. The final information entropy was very close to 8, and the correlation coefficient was approximately 0. All these tests verified the robustness and practicability of the proposed algorithm

Digital soil mapping of heavy metals using multiple geospatial data: Feature identification and deep neural network

Monitoring the spatial distribution and sources of heavy metals (HM) in soil is essential for avoiding health risks and achieving sustainable soil utilization. Multiple geospatial data, including remote sensing, climate, soil and topography data, were used to extract environmental covariates. Additionally, the spatial scene was employed as the alternative data of land use/land cover to describe the urban functions and human activity intensity in more detail. After converting to a uniform resolution of 30 m, these environmental covariates were adopted to characterize several common HM in soil, including copper (Cu), chromium (Cr), lead (Pb), nickel (Ni), and zinc (Zn). The RReliefF algorithm was used to identify several important variables. The quantification models of HM were established using back-propagation neural network (BPNN) and deep neural network (DNN). Besides, the impact of distance from the spatial scenes on HM were analyzed. The result demonstrated that the spatial scene is a key environmental covariate in estimating HM in soil. Compared with BPNN, the DNN model provided better accuracy (R2 = 0.67–0.75) for estimation of five HM elements. Therefore, the DNN model was used to map HM concentrations at a grid scale of 30 m. The spatial scenes with the highest risk of HM pollution are industrial areas, residential areas, road, and commercial areas, and the concentration of HM is negatively correlated with the distance from these spatial scenes. The effective impact distances of industrial and residential areas are about 2000 m, and the effective impact distances of road and commercial areas are 500 m

Correlating multi-scale structure characteristics to mechanical behavior of Caprinae horn sheaths

Horns are used by Bovidae animals for intraspecific combat; as such they are among Nature's toughest materials that require resistance to extreme loads. As a typical subfamily among Bovidae, Caprinae own light-wight horn with balanced strength and toughness. However, their structure and the salient mechanisms that underlie their mechanical behavior remain uncertain. This work clarifies the effect of multi-scale structure characteristics on mechanical behaviors of horn sheath by comparing Cashmere goat, White goat and Black sheep. With the methods of fractographic observations, conformational analysis, acoustic emission and finite element methods. Conformation of keratin and strength of fibre were proposed to influence the tensile/flexural performance a lot under both dried and hydrated condition. The corrugated lamellae structure was assumed to promote crack deflection and enhance dried samples, which showed more advantageous for applications of flexural loading. It is hard to impute the difference of mechanics to any one factor, and the synergism of multi-scale mechanisms is important to mechanical properties in Caprinae horn sheath. This research is expected to further encourage the horn-inspired design of secondary load-carrying lightweight composites