Journal
PHYSICAL REVIEW D
Volume 95, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.95.024031
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Funding
- Walter Burke Institute for Theoretical Physics at Caltech
- DOE [DE-SC0011632]
- Foundational Questions Institute
- Gordon and Betty Moore Foundation [776, GBMF-2644]
- John Simon Guggenheim Memorial Foundation
- Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF) [PHY-1125565]
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We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor product of factors, we consider a class of redundancy-constrained states in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein's equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. Aversion of the ER = EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.
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