Mutual Information in spacetime
Abstract
We compute mutual information for general spacetime regions using Sorkin's Gaussian field formalism. We show that this construction is naturally based on the reduced space of smearings that generate independent fields, making manifest that in QFTs with stress tensor the local algebras generated by regions sharing the same causal completion. We test the method for a Weyl fermion, the chiral current, and massless and massive real scalar fields across various spacetime regions in 1+1 Minkowski space. Across all cases, distinct spacelike-separated spacetime regions sharing the same causal completion yield identical mutual information. This formalism provides a setting in which to test the timelike tube theorem. Indeed, we observe that the mutual information of a timelike lens approaches that of its enveloping diamond as the cutoff is increased, offering a direct numerical verification of the theorem. In all the considered cases, our results agree with known continuum and spatial-lattice results. Finally, this work establishes a natural framework for studying entanglement measures in generalized free field theories, a task that is impractical within other existing prescriptions.
Related
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BibTeX
@misc{arias2026mutual,
title = {{Mutual Information in spacetime}},
author = {Raúl E. Arias and Marina Huerta and Pedro J. Martinez},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12047},
eprint = {2609.12047},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12047},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mutual Information in spacetime
AU - Raúl E. Arias
AU - Marina Huerta
AU - Pedro J. Martinez
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12047
UR - https://arxiv.org/abs/2609.12047
AB - We compute mutual information for general spacetime regions using Sorkin's Gaussian field formalism. We show that this construction is naturally based on the reduced space of smearings that generate independent fields, making manifest that in QFTs with stress tensor the local algebras generated by regions sharing the same causal completion. We test the method for a Weyl fermion, the chiral current, and massless and massive real scalar fields across various spacetime regions in 1+1 Minkowski space. Across all cases, distinct spacelike-separated spacetime regions sharing the same causal completion yield identical mutual information. This formalism provides a setting in which to test the timelike tube theorem. Indeed, we observe that the mutual information of a timelike lens approaches that of its enveloping diamond as the cutoff is increased, offering a direct numerical verification of the theorem. In all the considered cases, our results agree with known continuum and spatial-lattice results. Finally, this work establishes a natural framework for studying entanglement measures in generalized free field theories, a task that is impractical within other existing prescriptions.
ER -