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<p>We use large-<i>N</i> diagrammatic techniques to calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. These methods are specifically designed for symmetric sectors, allowing us to determine the relative entropy for random states exhibiting U(1) symmetry. This calculation serves as a measure of distinguishability within the symmetry sectors of random states. Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior. A remarkable finding is that relative entropies violate entanglement equipartition in the symmetry resolution for Haar-random states. Finally, we derive the symmetry-resolved Page curve. These results deepen our understanding of the properties of these random states.</p>

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Symmetry-resolved relative entropy of random states

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年4月11日

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  • Mostafa Ghasemi

摘要

We use large-N diagrammatic techniques to calculate the relative entropy of symmetric random states drawn from the Wishart ensemble. These methods are specifically designed for symmetric sectors, allowing us to determine the relative entropy for random states exhibiting U(1) symmetry. This calculation serves as a measure of distinguishability within the symmetry sectors of random states. Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior. A remarkable finding is that relative entropies violate entanglement equipartition in the symmetry resolution for Haar-random states. Finally, we derive the symmetry-resolved Page curve. These results deepen our understanding of the properties of these random states.