Symmetry-Resolved Relative Entropy of Random States
- URL: http://arxiv.org/abs/2411.01491v2
- Date: Wed, 27 Nov 2024 07:37:21 GMT
- Title: Symmetry-Resolved Relative Entropy of Random States
- Abstract summary: We calculate the relative entropy of symmetric random states drawn from the Wishart ensemble.<n>Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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. Furthermore, we derive the symmetry-resolved Page curve. These results deepen our understanding of the properties of these random states.
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