More of the bulk from extremal area variations

Bao, Ning; Cao, ChunJun; Fischetti, Sebastian; Pollack, Jason; Zhong, Yang

doi:10.1088/1361-6382/abcfd0

Cited by 14 publications

(18 citation statements)

References 76 publications

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“…(A.7) are redundant in this system. Equivalently, only the MMI inequalities together with the singleton instances of 17 Something analogous to what was explained in the previous footnote for the case of instances of SA happens for SSA as well. If e.g.…”

Section: Jhep11(2021)177mentioning

confidence: 52%

“…The RT formula, eq. (1.1), and its time-dependent [11] and quantum generalizations [12,13] have been exploited in various ways in the context of bulk reconstruction from boundary data [5][6][7][8][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…Note that there are inequalities that are not provable using the techniques of maximin[57] 7. In certain cases, uniqueness of such a geometry would be guaranteed by the results of refs [16,17]8.…”

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confidence: 99%

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Quantum Extremal Surfaces and the Holographic Entropy Cone

Akers

Hernández-Cuenca

Rath

2021

J. High Energ. Phys.

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Quantum states with geometric duals are known to satisfy a stricter set of entropy inequalities than those obeyed by general quantum systems. The set of allowed entropies derived using the Ryu-Takayanagi (RT) formula defines the Holographic Entropy Cone (HEC). These inequalities are no longer satisfied once general quantum corrections are included by employing the Quantum Extremal Surface (QES) prescription. Nevertheless, the structure of the QES formula allows for a controlled study of how quantum contributions from bulk entropies interplay with HEC inequalities. In this paper, we initiate an exploration of this problem by relating bulk entropy constraints to boundary entropy inequalities. In particular, we show that requiring the bulk entropies to satisfy the HEC implies that the boundary entropies also satisfy the HEC. Further, we also show that requiring the bulk entropies to obey monogamy of mutual information (MMI) implies the boundary entropies also obey MMI.

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Section: Jhep11(2021)177mentioning

confidence: 52%

Section: Introductionmentioning

confidence: 99%

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Quantum Extremal Surfaces and the Holographic Entropy Cone

Akers

Hernández-Cuenca

Rath

2021

J. High Energ. Phys.

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“…In this way, bulk spacetime dynamics arise from entanglement. Moreover, the bulk spacetime metric itself may be reconstructed solely from boundary entanglement [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Thus, in its deepest form, the RT prescription suggests spacetime connectivity emerges from entanglement [61][62][63][64][65], succinctly summarized by the slogan 'entanglement=geometry'.…”

Section: Jhep02(2022)093mentioning

confidence: 99%

Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Pedraza

Russo

Svesko

et al. 2022

J. High Energ. Phys.

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Holographic entanglement entropy was recently recast in terms of Riemannian flows or ‘bit threads’. We consider the Lorentzian analog to reformulate the ‘complexity=volume’ conjecture using Lorentzian flows — timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or ‘gatelines’. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific ‘canonical’ thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein’s equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of ‘spacetime complexity’. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [1], including several new results.

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“…See the discussion in section 5. As for the uniqueness[67] of the bulk metric reconstructed by the extremal surfaces, see[68] for its generalization to the case of the two-sided geometries.…”

mentioning

confidence: 99%