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

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 pro...

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Vydané v:Journal of King Saud University. Computer and information sciences Ročník 37; číslo 8; s. 247 - 20
Hlavní autori: Hao, Chaolong, Ma, Quangong, Chen, Yaqi, Zhang, Hao, Qu, Dan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.10.2025
Springer Nature B.V
Springer
Predmet:
Arbitrary states
Centroids
Coding
Computer Imaging
Computer Science
Controllability
Cryptography
Database Management
High-dimensional entangled state
Logic
Machine Learning
Methods
Multimedia
Network design
Neural networks
Original Paper
Orthogonal projection splitting structure
Pattern Recognition and Graphics
Perturbation
Quantum autoencoder
Quantum information hiding
Qubits (quantum computing)
Semantics
Software Engineering/Programming and Operating Systems
Steganography
Systems and Data Security
Theory of Computation
Vision
Quantum information hiding
Arbitrary states
High-dimensional entangled state
Orthogonal projection splitting structure
Quantum autoencoder
ISSN:1319-1578, 2213-1248, 1319-1578
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Abstract 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.
AbstractList Abstract While classical steganography achieves maturity in digital media, hiding arbitrary quantum states ( $$\alpha |0\rangle + \beta |1\rangle $$ 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 $$n \le 10$$ n ≤ 10 and perturbation strengths $$\varepsilon \in [0,1]$$ 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., $$n = 5, \varepsilon = 0.6$$ n = 5 , ε = 0.6 ), with fidelity values $$F\left( \rho _{\text {stego}}, \tilde{\rho }_{\text {stego}} \right) =0.91$$ F ρ stego , ρ ~ stego = 0.91 / $$F\left( \rho _{S}, \tilde{\rho }_{S} \right) =0.84$$ F ρ S , ρ ~ S = 0.84 providing a reference for network design. Finally, we extend the single-carrier (“ $$1+1$$ 1 + 1 ”) task to the multi-carrier (“ $$1+N$$ 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 $$n = 5$$ n = 5 and $$\varepsilon = 0.6$$ 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.
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 Fρstego,ρ~stego=0.91 / FρS,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.
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.
ArticleNumber 247
Author Chen, Yaqi
Qu, Dan
Ma, Quangong
Zhang, Hao
Hao, Chaolong
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Keywords Quantum information hiding
Arbitrary states
High-dimensional entangled state
Orthogonal projection splitting structure
Quantum autoencoder
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Snippet While classical steganography achieves maturity in digital media, hiding arbitrary quantum states ( α | 0 ⟩ + β | 1 ⟩ ) has emerged as an intriguing frontier....
While classical steganography achieves maturity in digital media, hiding arbitrary quantum states (α|0⟩+β|1⟩) has emerged as an intriguing frontier. To address...
Abstract While classical steganography achieves maturity in digital media, hiding arbitrary quantum states ( $$\alpha |0\rangle + \beta |1\rangle $$ α | 0 ⟩ +...
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StartPage 247
SubjectTerms Arbitrary states
Centroids
Coding
Computer Imaging
Computer Science
Controllability
Cryptography
Database Management
High-dimensional entangled state
Logic
Machine Learning
Methods
Multimedia
Network design
Neural networks
Original Paper
Orthogonal projection splitting structure
Pattern Recognition and Graphics
Perturbation
Quantum autoencoder
Quantum information hiding
Qubits (quantum computing)
Semantics
Software Engineering/Programming and Operating Systems
Steganography
Systems and Data Security
Theory of Computation
Vision
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Title Quantum autoencoder implementation of high-dimensional steganographic encoding for arbitrary quantum states
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