A novel and traceable quantum steganography scheme based on pixel value differencing (PVD) is proposed. In the proposed scheme, a quantum cover image is divided into non-overlapping blocks of two consecutive pixels. Then, by a series of reversible logic circuits, we calculate the difference value based on the values of the two pixels in each block and classify it as one of a set of continuous ranges. The secret image and operator information are embedded in the cover image by using the new obtained difference value to replace the original one. The number of bits of secret image that can be embedded in a block is determined, and the number of bits of operator information is decided by the range of the difference value belongs to. Moreover, when the embedded data is extracted from a stego image, it is not necessary to refer to the original cover image. The performance of the proposed scheme is based on the analysis of several categories of simulation results, such as visual quality, capacity, and robustness.