Quantum image processing is a system where both quantum computing and image processings are key. Now it is required to investigate how to apply image processing concepts such as image edge detection and improved Sobel operator, to quantum image processing. Just as traditional image processing helps to image manipulation, our efforts in quantum image processing contribute to the further development of quantum algorithm and quantum information theory. Edge detection is an important problem in traditional image processing, and image edge detection algorithm can filter image edge features and retain important attributes. We proposed a quantum edge detection algorithm, which employs improved Sobel operator to improve the performance, so as to solve the problem of unsatisfactory traditional image edge detection methods. In practical application, the amount of image data to be processed increases sharply, and the computing power of classical computer becomes a limitation. Quantum information processing can effectively accelerate many classical problems by virtue of quantum mechanical characteristics, such as quantum superposition, entanglement, parallelism. Our proposed method uses the novel enhanced quantum representation to store quantum images, which stores all the pixels in the image in a superimposed state, realizing parallel computation. The improved eight-direction Sobel operator is used to calculate the gray gradient, and the quantum circuit is designed to realize quantum edge detection. Simulation results have shown that our algorithm can extract edge with dimension 2n×2n when the computational complexity is O(n2+2q+3). The improved algorithm can detect more edge details and has strong adaptability.

As an important information medium, the digital image exists widely on the Internet. Quantum walks have the property of encrypting information. For the eneryption problem of optical digital images, an encryption scheme based on discrete cosine transform (DCT) and alternate quantum walks (AQW) is proposed in this paper. First, we use AQW and XOR operation to preprocess images in the spatial domain. Then, AQW are used to generate two random phase masks which can operate the preprocessed image and the DCT image, respectively. Finally, the encrypted image is obtained by using discrete cosine inverse exchange. The control parameters of AQW can replace the random phase mask as the key in the encryption and decryption process, so it is convenient for key management and transmission. The experimental simulation carried out the analysis of the image pixel histogram, the correlation of adjacent pixels, the robustness against noise and the sensitivity of secret keys, the results show that the image encryption method has strong security.

We investigate the properties of asymmetric quark matter and strange quark matter in the framework of the SU(3) Nambu–Jona-Lasinio (NJL) model with two types of vector interactions: (1) the flavor-dependent repulsion among different flavors of quarks with the coupling constant $G_V$, and (2) the universal repulsion and the vector-isovector interaction among different flavors of quarks with the coupling constants $g_V$ and $G_{IV}$. Using these two types of vector interactions in the NJL model, we study the quark symmetry energy in asymmetric quark matter, the constituent quark mass, the quark fraction, the equation of state in strange quark matter, the maximum mass of a quark star, and the properties of the QCD phase diagram. We find that including the two types of vector interactions in the SU(3) NJL model can significantly influence the quark matter symmetry energy as well as the properties of strange quark matter and quark stars. In particular, our results indicate that we can describe PSR $\mathrm{J}1614-2230$ and PSR $\mathrm{J}0348+0432$ as quark stars by considering the universal repulsion and the vector-isovector interaction among quark matter in the SU(3) NJL model.

This paper proposes an image encryption scheme based on a discrete-time alternating quantum walk (AQW) and the advanced encryption standard (AES). We use quantum properties to improve the AES algorithm, which uses a keystream generator related to AQW parameters to generate a probability distribution matrix. Some singular values of the matrix are extracted as the key to the AES algorithm. The Rcon of the AES algorithm is replaced with the elements of the probability distribution matrix. Then, the ascending order of the size of the clone probability distribution matrix scrambles the mapping rules of the S-box and ShiftRow transformations in the AES algorithm. The algorithm uses a probability distribution matrix and plaintext XOR operation to complete the preprocessing and uses the modified AES algorithm to complete the encryption process. The technology is based on simulation verification, including pixel correlation, histograms, differential attacks, noise attacks, information entropy, key sensitivity, and space. The results demonstrate a remarkable encryption effect. Compared with other improved AES algorithms, this algorithm has the advantages of the original AES algorithm and improves the ability to resist correlation attacks.

We extend the SU(3) Nambu–Jona-Lasinio (NJL) model to include two types of vector interaction. Using these two types of vector interaction in NJL mod