Entanglement Wedges for Gravitating Regions

• URL: http://arxiv.org/abs/2208.04993v4
• Date: Sat, 29 Jul 2023 01:07:47 GMT
• Title: Entanglement Wedges for Gravitating Regions
• Authors: Raphael Bousso and Geoff Penington
• Abstract summary: We conjecture that an arbitrary region $a$ can be assigned a generalized entanglement wedge $Esupset a$. We prove that $E$ satisfies a no-cloning theorem and appropriate forms of strong subadditivity and nesting. We propose that $E$ quantifies the range of holographic encoding, an important nonlocal feature of quantum gravity, in general spacetimes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by properties of tensor networks, we conjecture that an arbitrary gravitating region $a$ can be assigned a generalized entanglement wedge $E\supset a$, such that quasi-local operators in $E$ have a holographic representation in the full algebra generated by quasi-local operators in $a$. The universe need not be asymptotically flat or AdS, and $a$ need not be asymptotic or weakly gravitating. On a static Cauchy surface $\Sigma$, we propose that $E$ is the superset of $a$ that minimizes the generalized entropy. We prove that $E$ satisfies a no-cloning theorem and appropriate forms of strong subadditivity and nesting. If $a$ lies near a portion $A$ of the conformal boundary of AdS, our proposal reduces to the Quantum Minimal Surface prescription applied to $A$. We also discuss possible covariant extensions of this proposal, although none prove completely satisfactory. Our results are consistent with the conjecture that information in $E$ that is spacelike to $a$ in the semiclassical description can nevertheless be recovered from $a$, by microscopic operators that break that description. We thus propose that $E$ quantifies the range of holographic encoding, an important nonlocal feature of quantum gravity, in general spacetimes.

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