<p>Quantum watermarking serves as a pivotal technique for data concealment within quantum networks; facilitating secure communications by subtly embedding confidential data, such as private numbers, audio and images into digital carrier signals. This approach aims to maintain the integrity of quantum transmissions, while exerting minimal influence on the host signal. One aspect of watermarking, known as "echo hiding," involves integrating watermark data into a host audio signal, in the form of delays; also known as echoes. The bipolar echo hiding method introduces two symmetrical echoes with distinct delays. These parallel echoes are generated by echo kernels, with delays <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="607_2025_1422_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$d_{0}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="607_2025_1422_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">$d_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and amplitude amplification coefficients, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="607_2025_1422_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha_{1}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="607_2025_1422_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha_{2}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>. Separate quantum echoes are created and added to the original signal to accommodate <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="607_2025_1422_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\left| 0 \right.$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced open="|"> <mn>0</mn> </mfenced> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="607_2025_1422_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\left| 1 \right.$</EquationSource> <EquationSource Format="MATHML"><math> <mfenced open="|"> <mn>1</mn> </mfenced> </math></EquationSource> </InlineEquation> qubits. The bipolar echoes mitigate the distortion caused by the echo in the watermark signal, effectively cancelling out each other’s impact and enhancing signal transparency. In the extraction phase, the difference between the watermark and main signal is calculated and compared with the sum of the echo kernel. These sets are marked to recognize the watermark data. All quantum circuits have been simulated and demonstrated at the nanoscale. With an identical capacity (512 qbps), the bit error rate and signal-to-noise ratio of the proposed method have been compared with other quantum methods. The reported transparency of this method is 70.46 dB. A notable feature of this method is the robustness of the watermark signal against attacks.</p>

Towards secure quantum communication: a novel quantum audio watermarking based on bipolar echo hiding

期刊论文
发表日期：

2025年2月13日

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Masoumeh Velayatipour,
Mohammad Mosleh,
Mohsen Yoosefi Nejad,
Mohammad Kheyrandish

摘要

Quantum watermarking serves as a pivotal technique for data concealment within quantum networks; facilitating secure communications by subtly embedding confidential data, such as private numbers, audio and images into digital carrier signals. This approach aims to maintain the integrity of quantum transmissions, while exerting minimal influence on the host signal. One aspect of watermarking, known as "echo hiding," involves integrating watermark data into a host audio signal, in the form of delays; also known as echoes. The bipolar echo hiding method introduces two symmetrical echoes with distinct delays. These parallel echoes are generated by echo kernels, with delays $d_{0}$ $d_{0}$ and $d_{1}$ $d_{1}$ and amplitude amplification coefficients, $\alpha_{1}$ $α_{1}$ and $\alpha_{2}$ $α_{2}$ . Separate quantum echoes are created and added to the original signal to accommodate $\left| 0 \right.$ $|0)$ or $\left| 1 \right.$ $|1)$ qubits. The bipolar echoes mitigate the distortion caused by the echo in the watermark signal, effectively cancelling out each other’s impact and enhancing signal transparency. In the extraction phase, the difference between the watermark and main signal is calculated and compared with the sum of the echo kernel. These sets are marked to recognize the watermark data. All quantum circuits have been simulated and demonstrated at the nanoscale. With an identical capacity (512 qbps), the bit error rate and signal-to-noise ratio of the proposed method have been compared with other quantum methods. The reported transparency of this method is 70.46 dB. A notable feature of this method is the robustness of the watermark signal against attacks.