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<p>This paper introduces a new of quantum Tsallis entropy with localized characteristics. Specifically, we define and characterize a localized quantum Tsallis entropy using the local density operator constructed based on Local Quantum Bernoulli Noises (LQBNs). We also present some important properties of this entropy, including non-negativity, upper bound, unitarity invariance, and concavity. Notably, we find that local quantum Tsallis entropy does not satisfy additivity in general cases. However, under specific parameter conditions, namely when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_6070_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(q&gt;1\)</EquationSource> </InlineEquation>, it exhibits the property of subadditivity. The local quantum Tsallis entropy introduced in this paper not only enriches the theoretical framework of quantum entropy but also provides a powerful tool for describing the complexity of quantum states and understanding information transmission and distribution within quantum systems.</p>

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Quantum Tsallis Entropy with Localization Characteristics

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Qi Han,
  • Shuai Wang,
  • Lijie Gou,
  • Rong Zhang

摘要

This paper introduces a new of quantum Tsallis entropy with localized characteristics. Specifically, we define and characterize a localized quantum Tsallis entropy using the local density operator constructed based on Local Quantum Bernoulli Noises (LQBNs). We also present some important properties of this entropy, including non-negativity, upper bound, unitarity invariance, and concavity. Notably, we find that local quantum Tsallis entropy does not satisfy additivity in general cases. However, under specific parameter conditions, namely when \(q>1\) , it exhibits the property of subadditivity. The local quantum Tsallis entropy introduced in this paper not only enriches the theoretical framework of quantum entropy but also provides a powerful tool for describing the complexity of quantum states and understanding information transmission and distribution within quantum systems.