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arXiv:2312.14486 · Journal of High Energy Physics

Entanglement islands read perfect-tensor entanglement

Yi-Yu Lin, Jun Zhang, Jie-Chen Jin

Published Apr 19, 2024• 6 citations
arXivHTMLPDF

Abstract

A bstract In this paper, we make use of holographic Boundary Conformal Field Theory (BCFT) to simulate the black hole information problem in the semi-classical picture. We investigate the correlation between a portion of Hawking radiation and entanglement islands by the area of an entanglement wedge cross-section. Building on the understanding of the relationship between entanglement wedge cross-sections and perfect tensor entanglement as discussed in reference [18], we make an intriguing observation: in the semi-classical picture, the positioning of an entanglement island automatically yields a pattern of perfect tensor entanglement. Furthermore, the contribution of this perfect tensor entanglement, combined with the bipartite entanglement contribution, precisely determines the area of the entanglement wedge cross-section.

DOI
10.1007/jhep04(2024)113

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A bstract In this paper, we make use of holographic Boundary Conformal Field Theory (BCFT) to simulate the black hole information problem in the semi-classical picture. We investigate the correlation between a portion of Hawking radiation and entanglement islands by the area of an entanglement wedge cross-section. Building on the understanding of the relationship between entanglement wedge cross-sections and perfect tensor entanglement as discussed in reference [18], we make an intriguing observation: in the semi-classical picture, the positioning of an entanglement island automatically yields a pattern of perfect tensor entanglement. Furthermore, the contribution of this perfect tensor entanglement, combined with the bipartite entanglement contribution, precisely determines the area of the entanglement wedge cross-section.
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This thesis explores entanglement entropy, the black hole information paradox, and applications of physics-informed deep learning, with the Anti-de Sitter/conformal field theory (AdS/CFT) correspondence serving as a central framework. The first part examines entanglement islands as a possible resolution to the information paradox. Islands are surfaces in spacetime that contribute to purifying Hawking radiation in semi-classical gravity. We derive the entanglement entropy for annular entangling regions on d-dimensional AdS black hole backgrounds, and show that islands are highly sensitive to the underlying field theory modeling radiation - not only in details but in their very existence. Furthermore, we show how inhomogeneous transformations of entanglement entropy, via the replica trick, encode details about island formation, reflected in the stress tensor on both replica and base manifolds. We also introduce a framework for computing replica corrections to the thermal stress tensor, with intrinsic interest. To make contact with islands in positively curved spacetimes, we construct a multiverse model using T2-deformed dS wedge holography with dS Jackiw–Teitelboim gravity on infrared end-of-the-world branes, where finite-cutoff observers recover Page curves via islands. The second part investigates physics-informed neural networks (PINNs), which embed physical laws into the loss function. Motivated by the challenge of evaluating holographic entanglement entropy with sparse boundary data, we apply Bayesian PINNs (B-PINNs) to solve the corresponding nonlinear PDEs. The latter exemplifies high-energy theory complexities, extending PINNs beyond traditional engineering uses. We examine overconfidence in these models, attributing it to physical priors in the loss rather than miscalibration, and introduce diagnostic tools to assess this effect. Further, Hessian decomposition reveals how constraints hierarchically influence network behavior and shape the solution space, in a non-trivial way when varying with loss weight adjustments.
The entanglement wedge cross section in holographic picture provides a geometrical description of the entanglement for mixed states. In this paper we study the inequalities for the entanglement wedge cross section in AdS/BCFT duality. In the presence of the boundary in conformal field theory (CFT), the dual entanglement wedge cross section exhibits abundant phase structures since the extremal surface may end on the brane. We present a universal treatment which is applicable for all the possible phases such that the inequalities for the entanglement wedge cross section can be proved in an algebraic manner rather than a diagrammatic manner. We show that the entanglement wedge cross section in AdS/BCFT satisfies the same inequalities as in AdS/CFT.
A bstract We study the holographic duality between the reflected entropy and the entanglement wedge cross section with the first order correction. In the field theory side, we consider the reflected entropy for ρABm {\rho}_{AB}^m ρABm​ ρ AB m , where ρ AB is the reduced density matrix for two intervals in the ground state. The reflected entropy in the 2d holographic conformal field theories is computed perturbatively up to the first order in m − 1 by using the semiclassical conformal block. In the gravity side, we compute the entanglement wedge cross section in the backreacted geometry by cosmic branes with tension T m which are anchored at the AdS boundary. Comparing both results we find a perfect agreement, showing the duality works with the first order correction in m − 1.
Abstract We study the partial entanglement entropy (PEE) aspects of the holographic BCFT setup with an entanglement island, inspired by the holographic triality of the AdS/BCFT setup developed in the recent study on the black hole information problem, and the “PEE=CFF (component flow flux)” prescription, which is proposed recently to investigate the holographic PEE in the framework of bit thread formulation. Our study provides a bit thread description of the AdS/BCFT setup, which characterizes the specific entanglement details between the different parts of the system with an entanglement island, and may provide further insight into the black hole information problem. Furthermore, we show that in the context of island, one should distinguish between the fine-grained PEE and the semi-classical PEE. Interestingly, similar to the island rule of the fine-grained entropy in the semi-classical picture, we also propose the island rules of the fine-grained PEE.
A bstract In this paper, we study the holographic quantum entanglement structure in the finite-temperature CFT state/planar BTZ black hole correspondence from the perspective of entanglement threads. Unlike previous studies based on bit threads, these entanglement threads provide a more detailed characterization of the contribution sources to the von Neumann entropy of boundary subregions, in particular by quantitatively deriving the flux function of entanglement threads that traverse the wormhole horizon and connect the two asymptotic boundaries. Since entanglement threads are naturally and closely related to tensor network states, the results are argued to imply the existence of the perfect-type entanglement formed jointly by the entanglement threads crossing the wormhole and the internal threads in the single-sided boundary. We also discuss the close connections of this work with concepts such as bit threads and partial entanglement entropy.