A quantum watermarking scheme using simple and small-scale quantum circuits

A new quantum gray-scale image watermarking scheme by using simple and small-scale quantum circuits is proposed. The NEQR representation for quantum images is used. The image sizes for carrier and watermark are assumed to be $$2n \times 2n$$2n×2n and $$n \times n$$n×n, respectively. At first, a classical watermark with $$n \times n$$n×n image size and 8 bits gray scale is expanded to an image with $$2n \times 2n$$2n×2n image size and 2 bits gray scale. Then the expanded image is scrambled to be a meaningless image by the SWAP gates that controlled by the keys only known to the operator. The scrambled image is embedded into the carrier image by the CNOT gates (XOR operation). The watermark is extracted from the watermarked image by applying operations in the reverse order. Simulation-based experimental results show that our proposed scheme is excellent in terms of three items, visual quality, robustness performance under noises, and computational complexity.