Letter to the Editor regarding “Dynamic watermarking scheme for quantum images based on Hadamard transform” by Song et al.

et al. want to use quantum networks for arithmetic operation i.e., the plain adder network in Ref. [4] to realize the addition operation. As we know, the inputs of quantum gates of the quantum network are encoded in a binary form in the computational basis of quantum registers. The addition of two registers |a� and |b� can be written as |a, b� → |a, a+ b� . As one can reconstruct the input (a, b) out of the output (a, a + b), there is no loss of information, and the calculation can be implemented reversibly. By observing HT(|C�) and |PW〉, one can easily find that they are both multi-particle entangled states so that the plain adder network is invalid for implementing HT(|CW�) = HT(|C�)+ |PW�. Obviously, Song et al. neglected the constraint condition under which the plain adder network is used, that is, the inputs of two registers should be encoded in binary form in the computational basis states. To further understand the embedding procedure, we analyze the classical simulation procedure in Ref. [1]. By reimplementing the classical simulation procedure in Ref. [1], we can infer that Song et al. [1] in fact used the embedding strategy by adding the gray information of the watermark image to the amplitude of the HT of the quantum carrier image with a weight α. The similar problem occurs in the watermark image’s extracting phase. The embedder extracts the final watermark image by the following way: |W � = P(HT(|CW�) − HT(|C�)). By analyzing and reimplementing the classical simulation procedure in Ref. [1], we infer that the authors of Ref. [1] in fact implemented the extracting strategy by subtracting the carrier image from the embedded carrier image. Similar to the watermark embedding algorithm, the implementation of the transform |W � = P(HT(|CW�) − HT(|C�)) should also abide by the principles of quantum mechanics. That is, the quantum watermark extracting cannot be implemented Dear Sir,