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<p>In this work, we present the parameterized entanglement measures, <i>q</i>-concurrence with <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4692_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(q&gt;0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4692_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(q\not =1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>≠</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. And we derive analytical lower bounds for the entanglement measures by using positive partial transposition and realignment criteria, detailed examples are presented. Moreover, we show that the increase of <i>q</i>-concurrence <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4692_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="83" /> </InlineMediaObject> <EquationSource Format="TEX">\((1&lt;q&lt;2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>&lt;</mo> <mi>q</mi> <mo>&lt;</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for some superposition states are upper bounded by 1/2.</p>

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Parameterized entanglement measures with computable lower bounds

  • 期刊论文

  • 发表日期：

    2025年3月3日

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  • Gui Bao,
  • Xue-Na Zhu

摘要

In this work, we present the parameterized entanglement measures, q-concurrence with \(q>0\) q > 0 and \(q\not =1\) q ≠ 1 . And we derive analytical lower bounds for the entanglement measures by using positive partial transposition and realignment criteria, detailed examples are presented. Moreover, we show that the increase of q-concurrence \((1<q<2)\) ( 1 < q < 2 ) for some superposition states are upper bounded by 1/2.