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<p>For a quantum secret sharing scheme built from a general quantum stabilizer code, no measurement-free circuit has been known for reconstructing its quantum secrets, except particular classes, such as one proposed by Cleve, Gottesman and Lo. We propose a measurement-free reconstruction circuit of quantum secrets in quantum secret sharing based on stabilizer codes. Our reconstruction circuit has width <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4943_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(k+|J|\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>+</mo> <mo stretchy="false">|</mo> <mi>J</mi> <mo stretchy="false">|</mo> </mrow> </math></EquationSource> </InlineEquation> and consists of <i>O</i>(<i>k</i>|<i>J</i>|) one- or two-qudit unitary gates when |<i>J</i>| participants reconstruct <i>k</i>-qudit quantum secrets.</p>

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Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月29日

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  • Shogo Chiwaki,
  • Ryutaroh Matsumoto

摘要

For a quantum secret sharing scheme built from a general quantum stabilizer code, no measurement-free circuit has been known for reconstructing its quantum secrets, except particular classes, such as one proposed by Cleve, Gottesman and Lo. We propose a measurement-free reconstruction circuit of quantum secrets in quantum secret sharing based on stabilizer codes. Our reconstruction circuit has width \(k+|J|\) k + | J | and consists of O(k|J|) one- or two-qudit unitary gates when |J| participants reconstruct k-qudit quantum secrets.