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<p>In the present work, we introduce some analytical bounds for the Ramos disentropy and Renyi-based Ramos disentropy of the Wigner function. We will prove that the Lambert–Tsallis function <i>W</i><sub><i>q</i></sub> with <i>q</i> = 2 effectively characterizes the quasi-probability of Fock states. Inequalities for Ramos disentropy and Renyi-based Ramos disentropy in phase plane compact domains are obtained. At last, we will show that the essential norm of the Ramos disentropy for positive Wigner states is finite and an upper limit for Renyi-based disentropy is established in space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2024_4602_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}^{\alpha }({\mathbb{R}}^{d})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>L</mi> </mrow> <mi>α</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Bounds for disentropy of the Wigner function

  • 期刊论文

  • 发表日期：

    2025年1月30日

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  • J. L. E. da Silva,
  • D. C. Souza,
  • R. V. Ramos

摘要

In the present work, we introduce some analytical bounds for the Ramos disentropy and Renyi-based Ramos disentropy of the Wigner function. We will prove that the Lambert–Tsallis function Wq with q = 2 effectively characterizes the quasi-probability of Fock states. Inequalities for Ramos disentropy and Renyi-based Ramos disentropy in phase plane compact domains are obtained. At last, we will show that the essential norm of the Ramos disentropy for positive Wigner states is finite and an upper limit for Renyi-based disentropy is established in space \({L}^{\alpha }({\mathbb{R}}^{d})\) L α ( R d ) .