Reflected entropy in double holography

Ling, Yi; Liu, Peng; Liu, Yuxuan; Niu, Chao; Xian, Zhuo-Yu; Zhang, Cheng-Yong

doi:10.1007/jhep02(2022)037

Cited by 25 publications

(13 citation statements)

References 33 publications

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“…Meanwhile, higher dimensional black hole cases are considered in [41][42][43][44][45][46][47][48] as well as higher derivative gravity [49,50]. Interestingly, the page curve can be realized in the moving mirror scenario [51][52][53], and other quantum information or thermodynamic quantities except entanglement entropy are investigated within island formula [54][55][56][57][58][59][60][61][62].…”

Section: Introductionmentioning

confidence: 99%

The universality of islands outside the horizon

He,

Sun,

Zhao

et al. 2021

Preprint

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We systematically calculate the quantum extremal surface (QES) associated with Hawking radiation for general D-dimensional (D ≥ 2) asymptotically flat (or AdS) eternal black holes using the island formula. We collect the Hawking radiation particles by a non-gravitational bath and find that a QES exists in the near-horizon region outside the black hole when c • G (D) is smaller enough where c is the central charge of the conformal matter and G (D) the D-dimensional Newton constant. The locations of the QES in these backgrounds are obtained and the late-time radiation entropy saturates the two times of black hole entropy. Finally, we numerically check that the no island configuration exists once c•G (D) exceeds a certain upper bound in two-dimensional generalized dilaton theories (GDT).

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Section: Introductionmentioning

confidence: 99%

The universality of islands outside the horizon

He,

Sun,

Zhao

et al. 2021

Preprint

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“…As proposed previously in [37,68], we will still call the phases as shown in Fig. 5(a) and 5(c) the trivial phase and the island phase respectively, since the configurations of HRT surfaces are similar to the cases with one Planck brane.…”

Section: Quantum Extremal Surfaces and Phase Structuresmentioning

confidence: 99%

“…On one side, other measures were introduced to investigate the entanglement properties of radiation in [61][62][63][64][65][66][67]. On the other side, the entanglement properties inside the gravity system were studied in [68], where the emergence of the island trimmed off the growth of reflected entropy.…”

Section: Introductionmentioning

confidence: 99%

Black holes Entangled by Radiation

Liu,

Xian,

Peng

et al. 2022

Preprint

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We construct several models to describe the scenario where two eternal black holes are entangled by exchanging radiations. The increasing entanglement between two black holes is reflected in the emergence of a wormhole phase, which could be considered as an incarnation of ER = EP R conjecture. In the context of double holography, we compute the holographic entanglement entropy and the mutual information among of various partitions in the bulk and obtain the phase structure of the entanglement for the system. We find that two black holes, which could be either equal in size or not, can be entangled as long as they are not far apart; in general, the formation of a wormhole needs to overcome the distance between two black holes, and unitarity is preserved by either the formation of a wormhole or the emergence of islands. When the sizes of two black holes are not equal, we observe a loss of entanglement between the smaller black hole and the radiation at late times. We further compute the same entropy measures on the field theory side by considering a coupled SYK model at finite N , where two SYK models are applied as the dual description of two black holes and a Majorana chain connecting them resembles the radiation region. We explicitly compute the entanglement among two SYK systems and the chain, and obtain the similar phase structure as the bulk results. In general, a time delay of entanglement between two SYK sites is found in cases with longer Majorana chains. In particular, when two SYK sites are different in size, similar entanglement loss between the SYK cluster with fewer fermions and the radiation region are observed. To have a more intuitive understanding on the evolution of the entanglement, we further investigate a chain model composed of EPR clusters where exchanging particles are only allowed between neighbouring clusters. In this model, the outermost clusters serve as two black holes, and all inner clusters serve as the radiation. Despite the drastic simplification, the main features observed in previous models persist in this model, including the feature of entanglement between outermost clusters, the time delay of entanglement between two black holes due to distance, and the entanglement loss.

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“…[96]. For other recent comments on entanglement negativity and reflected entropy, see Refs [97][98][99][100][101][102][103][104].…”

Section: Introductionmentioning

confidence: 99%

Effective reflected entropy and entanglement negativity for general 2D eternal black holes

Jiong¹,

Lu²

2022

Preprint

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Both reflected entropy and entanglement negativity provide valid measures of entanglement between subsystems of a mixed state. For general 2D eternal black holes coupled with CFT matters in large c limit, we perform the replica-trick computation and find that both effective Renyi reflected entropy and effective entanglement negativity can be expressed in terms of the combination of modified backreacting cosmic branes in AdS 3 bulk. We then develop a holographic scheme to calculate effective reflected entropy and entanglement negativity for general 2D eternal black holes coupled with CFT matters in large c limit. Using the scheme, we check the consistency condition of the island formulae for entanglement negativity and reflected entropy. We find that the combinations of modified backreacting cosmic branes in AdS 3 bulk from the two island proposals of entanglement negativity exactly match with each other. Finally, we study the saturation of the reflected entropy inequality.

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Reflected entropy in double holography

Cited by 25 publications

References 33 publications

The universality of islands outside the horizon

The universality of islands outside the horizon

Black holes Entangled by Radiation

Effective reflected entropy and entanglement negativity for general 2D eternal black holes

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