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<p>Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6135_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>,<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6135_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation>)-relative entropy of coherence under mutually unbiased equiangular tight frames, and derive an interesting result for different parameters. As consequences, we obtain corresponding results under mutually unbiased bases, equiangular tight frames or based on Tsallis <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6135_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>-relative entropies and Rényi<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6135_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>-relative entropies. We illustrate the derived inequalities by explicit examples in two dimensional spaces, showing that the lower bounds can be regarded as good approximations to averaged coherence quantifiers under certain circumstances.</p>

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Uncertainty Relations for Unified (\(\alpha\),\(\beta\))-relative Entropy of Coherence Under Mutually Unbiased Equiangular Tight Frames

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Baolong Cheng,
  • Zhaoqi Wu

摘要

Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ( \(\alpha\) , \(\beta\) )-relative entropy of coherence under mutually unbiased equiangular tight frames, and derive an interesting result for different parameters. As consequences, we obtain corresponding results under mutually unbiased bases, equiangular tight frames or based on Tsallis \(\alpha\) -relative entropies and Rényi \(\alpha\) -relative entropies. We illustrate the derived inequalities by explicit examples in two dimensional spaces, showing that the lower bounds can be regarded as good approximations to averaged coherence quantifiers under certain circumstances.