Pseudoentropy sum rule by analytical continuation of the superposition parameter

Fuente: arXiv
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Main Authors: Guo, Wu-zhong, Jiang, Yao-zong, Xu, Jin
Format: Preprint
Published: 2024
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author Guo, Wu-zhong
Jiang, Yao-zong
Xu, Jin
author_facet Guo, Wu-zhong
Jiang, Yao-zong
Xu, Jin
contents In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of a superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density matrix of the superposition state can be treated in a unified manner. Within this framework, we naturally derive sum rules for the (reduced) transition matrix, pseudo Rényi entropy, and pseudoentropy. Furthermore, we demonstrate the close relationship between the sum rule for pseudoentropy and the singularity structure of the entropy function for the superposition state after analytical continuation. We also explore potential applications of the sum rule, including its relevance to understanding the gravity dual of non-Hermitian transition matrices and establishing upper bounds for the absolute value of pseudoentropy.
format Preprint
id arxiv_https___arxiv_org_abs_2405_09745
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Pseudoentropy sum rule by analytical continuation of the superposition parameter
Guo, Wu-zhong
Jiang, Yao-zong
Xu, Jin
High Energy Physics - Theory
Statistical Mechanics
Quantum Physics
In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of a superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density matrix of the superposition state can be treated in a unified manner. Within this framework, we naturally derive sum rules for the (reduced) transition matrix, pseudo Rényi entropy, and pseudoentropy. Furthermore, we demonstrate the close relationship between the sum rule for pseudoentropy and the singularity structure of the entropy function for the superposition state after analytical continuation. We also explore potential applications of the sum rule, including its relevance to understanding the gravity dual of non-Hermitian transition matrices and establishing upper bounds for the absolute value of pseudoentropy.
title Pseudoentropy sum rule by analytical continuation of the superposition parameter
topic High Energy Physics - Theory
Statistical Mechanics
Quantum Physics
url https://arxiv.org/abs/2405.09745