A secure controlled quantum image steganography scheme based on the multi-channel effective quantum image representation model

In this article, we introduce a multi-channel effective representation of quantum images (MCEQI) based on the improved flexible representation of quantum images (IFRQI) to facilitate the quantum analysis of colored digital images. We use an effective method to encode the intensity value of each pixel of a color digital image into a quantum state vector that yields a highly distinctive probability distribution in response to projective measurements, and thus allows for accurate restoration of the image information. In addition, we propose a high-capacity steganography scheme based on the MCEQI model. We embed the color information of a secret color image in the MCEQI state of a carrier color image by using controlled rotations. The sizes of the secret image and cover image are considered to be \(2^n\times 2^n\) and \(2^{n+1}\times 2^{n+1}\), respectively. We divide the red, green, and blue channel information of the secret image into four planes, each with a depth of 2 bits. For each plane, we construct an array of angle values that encode the color information. The encoded information is then embedded in the MCEQI state of the cover image using controlled rotations determined by the key K, derived from the fractional-order erbium-doped laser chaotic system. The process of extracting the secret image is the inverse of the embedding process and requires the inverse key \(K'\). Finally, we perform the analysis of the embedding capacity, time complexity, and visual effects to establish the effectiveness of the proposed steganography scheme.