Quantum Extremal Surfaces and the Holographic Entropy Cone

Akers, Chris; Hernández-Cuenca, Sergio; Rath, Pratik

doi:10.1007/jhep11(2021)177

Cited by 21 publications

(21 citation statements)

References 61 publications

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“…Our preliminary results suggest that the monogamy of mutual information can be derived using our quantum generalization of the max multiflow theorem, as was done in the classical case [64], although requiring a 'geometrization condition' for the bulk entropies. This is a sufficient condition in our proof, however, it certainly seems stronger than bulk JHEP02(2022)180 MMI (see, however [110]). There are reasons to further investigate this question, however, in order to clarify the consistency conditions of double holographic scenarios.…”

Section: Jhep02(2022)180mentioning

confidence: 77%

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Quantum bit threads and holographic entanglement

Agón

Pedraza

2022

J. High Energ. Phys.

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Quantum corrections to holographic entanglement entropy require knowledge of the bulk quantum state. In this paper, we derive a novel dual prescription for the generalized entropy that allows us to interpret the leading quantum corrections in a geometric way with minimal input from the bulk state. The equivalence is proven using tools borrowed from convex optimization. The new prescription does not involve bulk surfaces but instead uses a generalized notion of a flow, which allows for possible sources or sinks in the bulk geometry. In its discrete version, our prescription can alternatively be interpreted in terms of a set of Planck-thickness bit threads, which can be either classical or quantum. This interpretation uncovers an aspect of the generalized entropy that admits a neat information-theoretic description, namely, the fact that the quantum corrections can be cast in terms of entanglement distillation of the bulk state. We also prove some general properties of our prescription, including nesting and a quantum version of the max multiflow theorem. These properties are used to verify that our proposal respects known inequalities that a von Neumann entropy must satisfy, including subadditivity and strong subadditivity, as well as to investigate the fate of the holographic monogamy. Finally, using the Iyer-Wald formalism we show that for cases with a local modular Hamiltonian there is always a canonical solution to the program that exploits the property of bulk locality. Combining with previous results by Swingle and Van Raamsdonk, we show that the con- sistency of this special solution requires the semi-classical Einstein’s equations to hold for any consistent perturbative bulk quantum state.

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Section: Jhep02(2022)180mentioning

confidence: 77%

“…Very recently we became aware of[110] which claims that bulk monogamy is indeed enough to ensure boundary monogamy.…”

mentioning

confidence: 99%

Quantum bit threads and holographic entanglement

Agón

Pedraza

2022

J. High Energ. Phys.

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“…Other interesting classes of quantum states and constructs have been studied in the past, which suffer from the same rapidly increasing complexity as n increases. It would be interesting to explore if, upon symmetrizations, one can gain some further knowledge about the general-n structure of the cone of stabilizer states [28], the cone of linear rank inequalities [29], the cone of hypergraph entropies [30][31][32], the cone of topological links [33], or even the HEC under quantum corrections from bulk matter fields [34].…”

Section: Discussionmentioning

confidence: 99%

The Symmetrized Holographic Entropy Cone

Fadel,

Hernández-Cuenca

2021

Preprint

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The holographic entropy cone (HEC) characterizes the entanglement structure of quantum states which admit geometric bulk duals in holography. Due to its intrinsic complexity, to date it has only been possible to completely characterize the HEC for at most n = 5 numbers of parties. For larger n, our knowledge of the HEC falls short of incomplete: almost nothing is known about its extremal elements. Here, we introduce a symmetrization procedure that projects the HEC onto a natural lower dimensional subspace. Upon symmetrization, we are able to deduce properties that its extremal structure exhibits for general n. Further, by applying this symmetrization to the quantum entropy cone, we are able to quantify the typicality of holographic entropies, which we find to be exponentially rare quantum entropies in the number of parties.

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“…The RT/HRT and maximin prescription has led to stronger inequalities on the von Neumann entropy that do not hold for non holographic systems [64][65][66][67]. These inequalities haven't been shown to hold when we include quantum corrections via the QES prescription, however exploration in this direction was initiated in [87] where it was shown that if the bulk entropies obey the monogamy of mutual information [64] then the dual boundary entropies also obey the same.…”

Section: Maximin Vs Extremal: Strong Sub-additivity and Entanglement ...mentioning

confidence: 99%

Holographic spacetime, black holes and quantum error correcting codes: A review

Kibe,

Mandayam,

Mukhopadhyay

2021

Preprint

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This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of the Page curve of the Hawking radiation from black holes. We review quantum error correction and relevant recovery maps with toy examples based on tensor networks, and discuss how it provides the desired framework for bulk reconstruction in which apparent inconsistencies with properties of the operator algebra in the dual field theory are naturally resolved. The importance of understanding the modular flow in the dual field theory has been emphasized. We discuss how the state-dependence of reconstruction of black hole microstates can be formulated in the framework of quantum error correction with inputs from extremal surfaces along with a quantification of the complexity of encoding of bulk operators. Finally, we motivate and discuss a class of tractable microstate models of black holes which can illuminate how the black hole complementarity principle can emerge operationally without encountering information paradoxes, and provide new insights into generation of desirable features of encoding into the Hawking radiation.

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Quantum Extremal Surfaces and the Holographic Entropy Cone

Cited by 21 publications

References 61 publications

Quantum bit threads and holographic entanglement

Quantum bit threads and holographic entanglement

The Symmetrized Holographic Entropy Cone

Holographic spacetime, black holes and quantum error correcting codes: A review

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