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Non-Hermitian density matrices from timelike entanglement and wormholes

Jonathan Harper1, Taishi Kawamoto1,2,3, Ryota Maeda1, Nanami Nakamura1, and Tadashi Takayanagi1,4

  • 1Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan
  • 2The Hakubi Center for Advanced Research, Kyoto University, Yoshida Ushinomiyacho, Sakyoku, Kyoto 606-8501, Japan
  • 3Department of Physics, Kyoto University, Kyoto 606-8502, Japan
  • 4Inamori Research Institute for Science, 620 Suiginya-cho, Shimogyo-ku, Kyoto 600-8411, Japan

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Phys. Rev. D 113, 126017 – Published 11 June, 2026

DOI: https://doi.org/10.1103/j2xw-tcsb

Abstract

We extensively explore the connections between timelike entanglement and non-Hermitian density matrices in quantum many-body systems. We classify setups where we encounter non-Hermitian density matrices into two types: one is due to causal influences under unitary evolutions, and the other is due to nonunitary evolutions in non-Hermitian systems. We provide various examples of these setups including interacting harmonic oscillators, two dimensional conformal field theories, and holographic dualities. In them, we compute the timelike entanglement entropy and imagitivity, which measures how much density matrices are non-Hermitian. In both two classes, typical holographic examples are given by traversable AdS wormholes. We explain how causal influences in a wormhole dual to a pair of non-Hermitian quantum systems is possible even without interactions between them. We argue that to realize a traversable wormhole we need not only ordinary quantum entanglement but also timelike entanglement.

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Phys. Rev. D 113, 126017– Published 11 June, 2026
  • Received 19 February 2026
  • Accepted 27 April 2026
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