<p>In quantum mechanics, measurements of a quantum state in various directions yield distinct outcomes, a principle that forms the foundation of quantum communication theory. This paper expands upon this concept by introducing a method to modify generator projection directions (MGPD) within quantum stabilizer codes. Employing the Steane code ((7, 1, 3) code), as a fundamental carrier, we develop a novel scheme for direct quantum steganography across a single-type Pauli channel. The infeasibility of eavesdropping decoding under MGPD is proven. We detail the steganographic encoding and decoding schemes, corresponding quantum circuits, and eavesdropping detection principles. We also use a ‘Sudoku’-style strategy to balance steganographic error probabilities and provide the complete steganography protocol. Relative to existing studies, the MGPD method achieves embedding rates approaching and attaining the upper limit of the information capacity for the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4880_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="130" /> </InlineMediaObject> <EquationSource Format="TEX">$(n,k,d)=(7,1,3)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mn>7</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> code within a noise probability range of approximately <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4880_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="132" /> </InlineMediaObject> <EquationSource Format="TEX">$1/(n+1)=12.5\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>12.5</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. It also reduces the consumption of auxiliary keys from <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4880_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="78" /> </InlineMediaObject> <EquationSource Format="TEX">$O(\log {(N)})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>O</mi> <mo stretchy="false">(</mo> <mo>log</mo> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> to <i>O</i>(1), while enabling eavesdropping detection and steganography of arbitrary quantum states. We investigate its potential applications in quantum communication and assess its benefits in the context of secret information transmission and eavesdropping detection in noisy channels. Although the MGPD method incorporates certain idealized assumptions and limitations, it provides novel perspectives on the concealment of quantum information.</p>

Quantum direct steganography scheme based on modified generator projection directions of steane code over a single-type Pauli channel

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发表日期：

2025年8月19日

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Chaolong Hao,
Quangong Ma,
Dan Qu,
Dawei Shi,
Xukui Yang,
Buyu Liu

摘要

In quantum mechanics, measurements of a quantum state in various directions yield distinct outcomes, a principle that forms the foundation of quantum communication theory. This paper expands upon this concept by introducing a method to modify generator projection directions (MGPD) within quantum stabilizer codes. Employing the Steane code ((7, 1, 3) code), as a fundamental carrier, we develop a novel scheme for direct quantum steganography across a single-type Pauli channel. The infeasibility of eavesdropping decoding under MGPD is proven. We detail the steganographic encoding and decoding schemes, corresponding quantum circuits, and eavesdropping detection principles. We also use a ‘Sudoku’-style strategy to balance steganographic error probabilities and provide the complete steganography protocol. Relative to existing studies, the MGPD method achieves embedding rates approaching and attaining the upper limit of the information capacity for the $(n,k,d)=(7,1,3)$ $(n, k, d) = (7, 1, 3)$ code within a noise probability range of approximately $1/(n+1)=12.5\%$ $1 / (n + 1) = 12.5 %$ . It also reduces the consumption of auxiliary keys from $O(\log {(N)})$ $O (log (N))$ to O(1), while enabling eavesdropping detection and steganography of arbitrary quantum states. We investigate its potential applications in quantum communication and assess its benefits in the context of secret information transmission and eavesdropping detection in noisy channels. Although the MGPD method incorporates certain idealized assumptions and limitations, it provides novel perspectives on the concealment of quantum information.