Deriving the PEE proposal from the locking bit thread configuration

Lin, Yi-Yu; Sun, Jwo‐Shiun; Zhang, Jun

doi:10.1007/jhep10(2021)164

Cited by 16 publications

(23 citation statements)

References 54 publications

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“…In the purview of holography, one can consider the finer description offered by the Ryu-Takanayagi prescription to relate points on the minimal surface to the corresponding boundary points[23,48]. Explicit constructions of the entanglement contour and the PEE in terms of bit threads[49] are provided in[50][51][52][53] (also see[23,24,47,48]).…”

mentioning

confidence: 99%

Balanced Partial Entanglement and Mixed State Correlations

Camargo,

Nandy,

Wen

et al. 2022

Preprint

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Recently in Ref. [1], one of the authors introduced the balanced partial entanglement (BPE), which has been proposed to be dual to the entanglement wedge cross-section (EWCS). In this paper, we explicitly demonstrate that the BPE could be considered as a proper measure of the total intrinsic correlation between two subsystems in a mixed state. The total correlation includes certain crossing correlations which are minimized on some balance conditions. By constructing a class of purifications from Euclidean path-integrals, we find that the balanced crossing correlations show universality and can be considered as the generalization of the Markov gap for canonical purification. We also test the relation between the BPE and the EWCS in three-dimensional asymptotically flat holography. We find that the balanced crossing correlation vanishes for the field theory invariant under BMS 3 symmetry (BMSFT) and dual to the Einstein gravity, indicating the possibility of a perfect Markov recovery. We further elucidate these crossing correlations as a signature of tripartite entanglement and explain their interpretation in both AdS and non-AdS holography.

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mentioning

confidence: 99%

Balanced Partial Entanglement and Mixed State Correlations

Camargo,

Nandy,

Wen

et al. 2022

Preprint

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“…We propose that, reproducing the right enanglement contour should be a reasonable physical requirement. This is recently explored in [36] by applying the locking theorems [55,56] of bit threads to construct a concrete locking scheme for the RT surfaces in the entanglement wedge. In [57] two perturbations of the bit threads configurations are explicitly considered, one is the geodesic bit threads normal to the RT surface [54], which is consistent with our fine structure analysis [29] 7 .…”

Section: Discussionmentioning

confidence: 99%

“…The fourth proposal [21] follows the construction of the extensive (or additive) mutual information (EMI) [31] (see also [32] for a similar construction), which tried to solve the above seven requirements in CFT. The entanglement contour can also be studied under the picture of the bit threads [33] in holographic theories, see for example [19,[34][35][36]. The PEE calculated by different approaches are highly consistent with each other [14,17,21,28,29], which implies the PEE should be unique and well defined.…”

Section: Upper Bound : Smentioning

confidence: 91%

First Law and Quantum Correction for Holographic Entanglement Contour

Han,

Wen

2021

Preprint

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Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region A to the first order perturbation of the expectation value of the modular Hamiltonian, δS A = δ K A . We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. δs A (x) = δ k A (x) . Here the contour functions s A (x) and k A (x) capture the contribution from the degrees of freedom at x to S A and K A respectively. In some simple cases k A (x) is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the ALC proposal shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the ALC proposal applies.

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“…Its formal proof involves further elements from convex optimization and convex relaxation, as well as strong duality [63]. This new prescription has helped uncover aspects of holographic entanglement and related quantities that were previously unknown, and has provided a nice information-theoretic interpretation of various known properties [64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83]. Similar to the RT formula, the bit thread formulation of holographic entanglement entropy has been generalized to the covariant settings [84] and for CFTs dual to higher curvature gravities [85], though, a version that incorporates quantum or 1/N corrections has not been worked out.…”

Section: Jhep02(2022)180mentioning

confidence: 99%

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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Deriving the PEE proposal from the locking bit thread configuration

Cited by 16 publications

References 54 publications

Balanced Partial Entanglement and Mixed State Correlations

Balanced Partial Entanglement and Mixed State Correlations

First Law and Quantum Correction for Holographic Entanglement Contour

Quantum bit threads and holographic entanglement

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