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  • Open Access

Relation between time- and spacelike entanglement entropy

Wu-zhong Guo1,*, Song He2,3,4,†, and Yu-Xuan Zhang4,‡

  • *Contact author: wuzhong@hust.edu.cn
  • †Contact author: hesong@jlu.edu.cn
  • ‡Contact author: yuxuanz20@mails.jlu.edu.cn
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Phys. Rev. D 112, 086020 – Published 29 October, 2025

DOI: https://doi.org/10.1103/gmkp-lrh3

Abstract

In this study, we establish a connection between time- and spacelike entanglement entropy. We show that timelike entanglement entropy is closely related to spacelike entanglement entropy and its temporal derivative. For a broad class of states, it can be uniquely determined by a linear combination of spacelike entanglement entropy and its first-order temporal derivative. This relation holds, for instance, in states conformally equivalent to the vacuum in two-dimensional conformal field theories. For more general states, we demonstrate that the relation can be constructed perturbatively. Our results suggest that timelike entanglement entropy is constrained by causality. Moreover, this relation provides a unified framework for time- and spacelike entanglement entropy, within which the imaginary component of timelike entanglement entropy can be understood as arising from the noncommutativity between the twist operator and its first-order temporal derivative.

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Phys. Rev. D 112, 086020– Published 29 October, 2025
  • Received 17 March 2024
  • Accepted 9 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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