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Journal of King Saud University - Computer and Information Sciences

Quantum autoencoder implementation of high-dimensional steganographic encoding for arbitrary quantum states

Chaolong Hao, Quangong Ma, Yaqi Chen, Hao Zhang, Dan Qu

Published Oct 1, 2025• 1 citation
Publisher

Abstract

While classical steganography achieves maturity in digital media, hiding arbitrary quantum states ( $$\alpha |0\rangle + \beta |1\rangle $$ ) 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 $$n \le 10$$ and perturbation strengths $$\varepsilon \in [0,1]$$ , 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., $$n = 5, \varepsilon = 0.6$$ ), with fidelity values $$F\left( \rho _{\text {stego}}, \tilde{\rho }_{\text {stego}} \right) =0.91$$ / $$F\left( \rho _{S}, \tilde{\rho }_{S} \right) =0.84$$ 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 $$\varepsilon = 0.6$$ , 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.

DOI
10.1007/s44443-025-00274-1

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Steganography is the art of concealing secret information by embedding it in an apparently innocent-looking message. Quantum steganography applies the principles of quantum mechanics to traditional steganography and, compared to the latter, offers significant advantages, including heightened security, improved concealment, and increased data-hiding capacity. Traditionally, quantum steganography disguises the covert communication as channel noise, which is corrected using preshared classical randomness. This method requires the steganalytic eavesdropper Eve to overestimate the level of channel noise, so that the bounds on the stego channel capacity depend on this assumed gap in Eve's knowledge of the channel. In this work, we point out that by means of preshared quantum entanglement the secret message can be encoded into nonlocal correlations, obviating the need for such an assumption of Eve's ignorance. Consequently, the capacity bounds on the stego channel can then come from the channel capacity of the quantum communication channel. We introduce three such entanglement-based quantum steganographic protocols that make use of catalytic quantum error-correcting codes (QECCs), degenerate entanglement-assisted QECCs, or the phase bit of preshared entanglement. Here catalytic QECCs enable recycling entanglement, while entanglement assistance allows both sender and receiver to contribute to the protocol's secrecy. We derive upper and lower bounds on the secrecy capacity of each protocol, and demonstrate their practical robustness.
End-to-end radio communication needs to be optimized against noisy channel conditions and other distortion effects. This paper presents a novel concept, a set of hybrid quantum-classical autoencoder architectures with a comprehensive feasibility study using standard encoded radio signals, to evaluate quantum neural network design requirements for the radio context. The hybrid scenarios include single-sided, i.e., quantum encoder (transmitter) or quantum decoder (receiver), as well as fully quantum radio channel autoencoder (transmitter-receiver) systems. We provide detailed formulas for each scenario and validate our model through an extensive set of simulations. Our results demonstrate model robustness and adaptability. Supporting experiments are conducted utilizing 4 and 16 Quadrature Amplitude Modulation schemes and we expect that the model is adaptable to more general encoding schemes. We explore model performance against both additive white Gaussian noise and Rayleigh fading models. Our numerical findings highlight the importance of designing efficient quantum neural network architectures for meeting application performance constraints – including data re-uploading methods, encoding schemes, and core layer structures.
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Currently, quantum steganography schemes utilizing the least significant bit (LSB) approach are primarily optimized for fixed-point data processing, yet they encounter precision limitations when handling extended floating-point data structures owing to quantization error accumulation. To overcome precision constraints in quantum data hiding, the EPlsb-MFQS and MVlsb-MFQS quantum steganography algorithms are constructed based on the LSB approach in this study. The multichannel floating-point quantum representation of digital signals (MFQS) model enhances information hiding by augmenting the number of available channels, thereby increasing the embedding capacity of the LSB approach. Firstly, we analyze the limitations of fixed-point signals steganography schemes and propose the conventional quantum steganography scheme based on the LSB approach for the MFQS model, achieving enhanced embedding capacity. Moreover, the enhanced embedding efficiency of the EPlsb-MFQS algorithm primarily stems from the superposition probability adjustment of the LSB approach. Then, to prevent an unauthorized person easily extracting secret messages, we utilize channel qubits and position qubits as novel carriers during quantum message encoding. The secret message is encoded into the signal’s qubits of the transmission using a particular modulo value rather than through sequential embedding, thereby enhancing the security and reducing the time complexity in the MVlsb-MFQS algorithm. However, this algorithm in the spatial domain has low robustness and security. Therefore, an improved method of transferring the steganographic process to the quantum Fourier transformed domain to further enhance security is also proposed. This scheme establishes the essential building blocks for quantum signal processing, paving the way for advanced quantum algorithms. Compared with available quantum steganography schemes, the proposed steganography schemes achieve significant improvements in embedding efficiency and security. Finally, we theoretically delineate, in detail, the quantum circuit design and operation process.