Pure states for subregions in gravity and their entanglement entropy

• URL: http://arxiv.org/abs/2606.03977v1
• Date: Tue, 02 Jun 2026 17:56:33 GMT
• Title: Pure states for subregions in gravity and their entanglement entropy
• Abstract summary: It is proposed that spatial subregions in quantum gravity can be assigned pure states, rather than mixed reduced density matrices.<n>The state is prepared by a partially frozen gravitational path integral, in which a spacetime subregion containing the spatial subregion is fixed while the field configurations and ambient geometry are summed over.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is proposed that spatial subregions in quantum gravity can be assigned pure states, rather than mixed reduced density matrices. The state is prepared by a partially frozen gravitational path integral, in which a spacetime subregion containing the spatial subregion is fixed while the field configurations and ambient geometry are summed over. In the semiclassical regime, we further propose a holographic prescription for the entanglement entropy of bipartitions of this state, with a frozen-region analogue of the homology constraint. The prescription satisfies nontrivial self-consistency conditions, including strong subadditivity, complementarity, and entanglement wedge nesting, and reproduces several known entropy formulas in holography and gravity as special cases. The construction suggests an observer-dependent entanglement wedge labeled by the frozen subregion.

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