Quantum Bousso bound

Strominger, Andrew; Thompson, David Mattoon

doi:10.1103/physrevd.70.044007

Cited by 58 publications

(104 citation statements)

References 16 publications

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“…As the UV cutoff length is taken to zero, we find an infinite-dimensional Hilbert space in any QFT, and the entropy of a region of space will generically diverge. Nevertheless, QFT reasoning can be used to derive a quantum version of the Bousso bound [46][47][48], by positing that the relevant entropy is not the full entanglement entropy, but the vacuum-subtracted or "Casini" entropy [49]. Given the reduced density matrix ρ A in some region A, and the reduced density matrix σ A that we would obtain had the system been in its vacuum state, the Casini entropy is given by…”

Section: A Gravity and Entropy Boundsmentioning

confidence: 99%

“…Since our original perturbation δS decreases the boundary area of our region, we expect the fieldtheory entropy to increase. This accounts for the minus sign in (46). Plugging (46) into (36) produces a relation between the local scalar curvature of a region around p and the change in the entropy of the EFT state on the background:…”

Section: A Renormalization and The Low Energy Effective Theorymentioning

confidence: 99%

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Space from Hilbert space: Recovering geometry from bulk entanglement

2017

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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. A version 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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Section: A Gravity and Entropy Boundsmentioning

confidence: 99%

Section: A Renormalization and The Low Energy Effective Theorymentioning

confidence: 99%

Space from Hilbert space: Recovering geometry from bulk entanglement

2017

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“…This version was proven for free and interacting theories in the G → 0 limit from the monotonicity property of the relative entropy [33,34]. Alternatively, Strominger and Thompson [14] suggested focussing on the case where any cut of the null surface N is closed and bounds a spacelike surface. One may then discuss the von Neumann entropy S vN of the region enclosed, and replace the "flux of entropy across N " with the change in S vN between the initial and final surfaces.…”

Section: Violating the Generalized Covariant Entropy Boundmentioning

confidence: 99%

Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions

Koeller

Marolf

2017

Class. Quantum Grav.

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Abstract:We study the Quantum Focussing Conjecture (QFC) in curved spacetime. Noting that quantum corrections from integrating out massive fields generally induce a Gauss-Bonnet term, we study Einstein-Hilbert-Gauss-Bonnet gravity and show for d ≥ 5 spacetime dimensions that weakly-curved solutions can violate the associated QFC for either sign of the Gauss-Bonnet coupling. The nature of the violation shows that -so long as the Gauss-Bonnet coupling is non-zero -it will continue to arise for local effective actions containing arbitrary further higher curvature terms, and when gravity is coupled to generic d ≥ 5 theories of massive quantum fields. The argument also implies violations of a recently-conjectured form of the generalized covariant entropy bound. The possible validity of the QFC and covariant entropy bound in d ≤ 4 spacetime dimensions remains open.

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“…T is the matter stress tensor component in the light-sheet direction, plus a shear-squared term that is associated with gravitational radiation. Using precise definitions of S [10][11][12][13][14][15][18][19][20], the G → 0 limit yields novel, highly nontrivial statements about quantum field theory: a Quantum Bousso Bound (QBB) [13], and the Quantum Null Energy Condition (QNEC) [15]. One can also consider the Generalized Second Law in this limit [12,20].…”

mentioning

confidence: 99%

Asymptotic entropy bounds

Bousso

2016

Phys. Rev. D

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We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focussing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the Quantum Null Energy Condition, of the Generalized Second Law, and of the Quantum Bousso Bound. CONTENTS

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Quantum Bousso bound

Cited by 58 publications

References 16 publications

Space from Hilbert space: Recovering geometry from bulk entanglement

Space from Hilbert space: Recovering geometry from bulk entanglement

Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions

Asymptotic entropy bounds

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