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arXiv:2512.13800 · Physical review. D/Physical review. D.

Non-hermitian Density Matrices from Time-like Entanglement and Wormholes

Jonathan Harper, Taishi Kawamoto, Ryota Maeda, Nanami Nakamura, Tadashi Takayanagi

hep-thcond-mat.stat-mechquant-phSubmitted Dec 15, 2025• Announced Dec 17, 2025• 1 citation• Revised Feb 16, 2026 (v2)
v1 · Dec 15, 2025v2 · Feb 16, 2026
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Abstract

We extensively explore the connections between time-like 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 non-unitary 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 time-like 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 time-like entanglement.

Comments
35 pages, 29 figures. v2: minor corrections and updates to presentation

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In this paper, we investigate entanglement for causally connected subregions A and B in quantum field theory and holography. Recent developments have established that a transition operator T A B can be well-defined for such subregions, which is generally non-Hermitian. By employing the Schwinger-Keldysh formalism and the real-time replica method, we show how to construct T A B and compute associated entanglement measures. In certain configurations, this leads to a notion of timelike entanglement entropy, for which we provide explicit quantum field theory computations and propose a holographic dual via analytic continuation from the Euclidean setup. Both analytical and numerical results are compared and found consistent. If entanglement between causally connected subregions is to be meaningful, it should admit well-defined extensions of other entanglement measures beyond the spacelike setting. With this motivation we study the analytic continuation of the twist correlators for reflected-entropy and propose a holographic geometric analog in complexified bulk geometry, providing evidence that entanglement measures can be extended to timelike regions.