Quantum autoencoder implementation of high-dimensional steganographic encoding for arbitrary quantum states - Hao, Chaolong; Ma, Quangong; Chen, Yaqi; Zhang, Hao; Qu, Dan (Journal of King Saud University. Computer and information sciences, 2025)
While classical steganography achieves maturity in digital media, hiding arbitrary quantum states ( α | 0 ⟩ + β | 1 ⟩ ) has emerged as an intriguing frontier. To address this problem, we establish a formal model of controllable random perturbation unitaries for single/multi-stego state tasks. We progressively explore Quantum Autoencoder (QAE) structures through three stages: starting from single-state scenarios without perturbation, advancing to perturbed conditions, and finally extending to multi-state tasks. We design two perturbation-based encoding schemes using Quantum Autoencoders (QAE): the simple scheme (QAE-DD) leverages the inverse application of encoding–decoding modules, while the improved scheme (QAE-OSP) incorporates orthogonal projection routing and parallel subnetworks to restructure the hidden-layer architecture. In 3-qubit entangled-state simulations with data scales n ≤ 10 and perturbation strengths ε ∈ [ 0 , 1 ] , QAE-DD performs well under low perturbation, whereas QAE-OSP maintains higher fidelity between the carrier and secret states under high perturbation conditions (e.g., n = 5 , ε = 0.6 ), with fidelity values F ρ stego , ρ ~ stego = 0.91 / F ρ S , ρ ~ S = 0.84 providing a reference for network design. Finally, we extend the single-carrier (“ 1 + 1 ”) task to the multi-carrier (“ 1 + N ”) scenario by constructing a “centroid” state training set based on the principal component of carrier-state groups and validating the applicability of both models. Under the conditions n = 5 and ε = 0.6 , the QAE-OSP model successfully improves the average fidelity between multiple secret states and carrier states from 0.68 to 0.90, demonstrating its capability to aggregate multiple carriers to enhance overall concealment. Although the present study covers only small-scale data and networks, it lays the groundwork for a neural network framework that covertly embeds arbitrary quantum states into high-dimensional quantum states, providing a basis for future exploration.