To address the problem that existing quantum image watermarking schemes have only a single watermarking mode with weak robustness, in this paper we propose a novel Multi-Modal Quantum Watermarking (MMQW) scheme using the generalized model of novel enhanced quantum representation. Our scheme provides four quantum watermarking modes (G_G, G_C, C_C, C_G), covering both types of grayscale and color images for the watermark and the carrier image. To enhance the robustness, we propose the Block Bit-plane Centrosymmetric Expansion (BBCE) method, which utilizes controlled quantum gates to extend the watermark, making our method resistant to noise and geometric attacks. Moreover, we propose a Brightness-based Watermarking Mechanism (BWM) for embedding and extraction. By uniform embedding, BWM not only minimizes the impact on the carrier image but also reduces the visual distortion of the extracted watermark. In the proposed MMQW, we implement three adaptive embedding strategies using controlled quantum gates, each of which is adaptively triggered according to the corresponding modalities. Detailed quantum circuits for quantum computing are provided. To evaluate imperceptibility and robustness of the MMQW, we conduct experiments using high-resolution images from the USC-SIPI dataset. The results show that PSNR of the watermarked image ranges from 36 dB to 56 dB, indicating the high visual quality. The PSNR of the extracted watermark is about 34 dB when the noise density is 0.05, while the PSNR is higher than 48 dB under common quantum rotation attacks, which indicate the high robustness against noise addition and geometric attacks. In addition, the proposed MMQW can resist to cropping attack with cropping percentage up to 55%. A comprehensive comparison with existing state-of-the-art works shows that our method has significant advantages.

中文翻译：

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MMQW：多模态量子水印方案

针对现有量子图像水印方案水印模式单一、鲁棒性差的问题，本文提出了一种利用新型增强量子表示的广义模型的多模态量子水印（MMQW）方案。我们的方案提供了四种量子水印模式（G_G、G_C、C_C、C_G），涵盖水印和载体图像的灰度和彩色图像。为了增强鲁棒性，我们提出了块位平面中心对称扩展（BBCE）方法，该方法利用受控量子门来扩展水印，使我们的方法能够抵抗噪声和几何攻击。此外，我们提出了一种用于嵌入和提取的基于亮度的水印机制（BWM）。通过均匀嵌入，BWM不仅最大限度地减少了对载体图像的影响，而且减少了提取的水印的视觉失真。在所提出的 MMQW 中，我们使用受控量子门实现了三种自适应嵌入策略，每个策略都根据相应的模态自适应触发。提供了用于量子计算的详细量子电路。为了评估 MMQW 的不可感知性和鲁棒性，我们使用 USC-SIPI 数据集的高分辨率图像进行实验。结果表明，水印图像的 PSNR 范围为 36 dB 至 56 dB，视觉质量较高。当噪声密度为0.05时，提取的水印的PSNR约为34 dB，而在常见的量子旋转攻击下，PSNR高于48 dB，这表明对噪声添加和几何攻击具有较高的鲁棒性。此外，所提出的MMQW可以抵抗裁剪攻击，裁剪百分比高达55%。与现有最先进作品的全面比较表明我们的方法具有显着的优势。