Neural-enabled quantum information hiding with error-correcting codes: a novel framework for arbitrary quantum state embedding

Abstract

Quantum information hiding, as an extension of classical information hiding techniques into the realm of quantum information, currently focuses on embedding classical bits (0/1) within quantum carriers. This includes methods such as disguising classical secret information as channel noise and embedding it within quantum error correction codes. However, the embedding mechanism for arbitrary quantum states \(\alpha |0\rangle + \beta |1\rangle \) is still in the exploratory stage. This paper proposes an innovative framework that leverages the redundant space of quantum error correction codes to construct a nonlinear decoding architecture with quantum neural networks. This approach simultaneously achieves both carrier state error correction and secret state embedding and extraction functions. Specifically, the [5,1,3] stabilizer code is used as the carrier, with secret state embedding achieved through single-qubit substitution, and a quantum autoencoder is designed for steganographic state information decoding. The proposed framework features fully quantum-based input/output systems, overcoming the limitations of traditional variational quantum circuits that rely on probabilistic measurements for output generation. By performing full ground-state measurements at the autoencoder bottleneck layer and optimizing the parallel sub-network architecture, the network achieves efficient convergence and effective extraction of single-copy quantum states. Experimental results show that under the conditions of optimized parameters and data size of 20, the training losses for the carrier and secret states are 0.03 and 0.08, respectively, with test fidelities of 0.92 and 0.93. For a data size of 50, the secret states recovery fidelity exceeds 0.87. KS test analysis indicates that the full ground-state measurement and parallel sub-network are key strategies for achieving network performance. Equivalent error analysis shows that this approach successfully utilizes the potential redundant space of quantum error correction codes, providing new research directions for quantum state information hiding.