The development of quantum image representation and quantum measurement techniques has made quantum image processing research a hot topic. In this paper, a novel Adaptive Quantum Scaling Model (AQSM) is first proposed for scrambling watermark images. Then, on the basis of the proposed AQSM, a novel quantum watermarking scheme is presented. Unlike existing quantum watermarking schemes with fixed embedding scales, the proposed method can flexibly embed watermarks of different sizes. In order to improve the robustness of the watermarking algorithm, a novel Histogram Distribution-based Watermarking Mechanism (HDWM) is proposed, which utilizes the histogram distribution property of the watermark image to determine the embedding strategy. In order to improve the accuracy of extracted watermark information, a quantum refining method is suggested, which can realize a certain error correction. The required key quantum circuits are designed. Finally, the effectiveness and robustness of the proposed quantum watermarking method are evaluated by simulation experiments on three image size scales. The results demonstrate the invisibility and good robustness of the watermarking algorithm.

翻译：量子图像表示与量子测量技术的发展使量子图像处理研究成为热点。本文首先提出了一种新颖的自适应量子缩放模型（AQSM）用于置乱水印图像。随后，在AQSM基础上提出了一种创新的量子水印方案。与现有固定嵌入尺度的量子水印方案不同，本方法能够灵活嵌入不同尺寸的水印。为提升水印算法的鲁棒性，提出基于直方图分布的水印机制（HDWM），该机制利用水印图像的直方图分布特性确定嵌入策略。为提高提取水印信息的准确性，提出量子精化方法以实现一定程度的误差校正。文中设计了所需的关键量子电路。最后通过三种图像尺寸尺度的仿真实验评估了所提量子水印方法的有效性与鲁棒性。结果表明该水印算法具有不可见性和良好的鲁棒性。