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Статті в журналах з теми "Entanglement in holography"

Автор: Grafiati

Опубліковано: 10 березня 2023

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1

Defienne, Hugo, Bienvenu Ndagano, Ashley Lyons, and Daniele Faccio. "Polarization entanglement-enabled quantum holography." Nature Physics 17, no. 5 (February 4, 2021): 591–97. http://dx.doi.org/10.1038/s41567-020-01156-1.

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2

Pakman, Ari, and Andrei Parnachev. "Topological entanglement entropy and holography." Journal of High Energy Physics 2008, no. 07 (July 22, 2008): 097. http://dx.doi.org/10.1088/1126-6708/2008/07/097.

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3

Obregón, O. "Generalized Entanglement Entropy and Holography." Journal of Physics: Conference Series 1010 (April 2018): 012009. http://dx.doi.org/10.1088/1742-6596/1010/1/012009.

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4

Jensen, Kristan, and Julian Sonner. "Wormholes and entanglement in holography." International Journal of Modern Physics D 23, no. 12 (October 2014): 1442003. http://dx.doi.org/10.1142/s0218271814420036.

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In this paper, we consider highly entangled states in theories with a gravity dual, where the entangled degrees of freedom are causally disconnected from each other. Using the basic rules of holography, we argue that there is a nontraversable wormhole in the gravity dual whose geometry encodes the pattern of the entanglement.

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5

Giataganas, D., and N. Tetradis. "Entanglement entropy, horizons and holography." Physics Letters B 796 (September 2019): 88–92. http://dx.doi.org/10.1016/j.physletb.2019.07.019.

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6

Gan, Wen-Cong, and Fu-Wen Shu. "Holography as deep learning." International Journal of Modern Physics D 26, no. 12 (October 2017): 1743020. http://dx.doi.org/10.1142/s0218271817430209.

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Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method [G. Carleo and M. Troyer, Science 355 (2017) 602, arXiv:1606.02318.] The power of deep neural network (DNN) based on deep learning is clarified by mapping it to renormalization group (RG), which may shed lights on holographic principle by identifying a sequence of RG transformations to the AdS geometry. In this paper, we show that any network which reflects RG process has intrinsic hyperbolic geometry, and discuss the structure of entanglement encoded in the graph of DNN. We find the entanglement structure of DNN is of Ryu–Takayanagi form. Based on these facts, we argue that the emergence of holographic gravitational theory is related to deep learning process of the quantum-field theory.

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7

Schwimmer, A., and S. Theisen. "Entanglement entropy, trace anomalies and holography." Nuclear Physics B 801, no. 1-2 (September 2008): 1–24. http://dx.doi.org/10.1016/j.nuclphysb.2008.04.015.

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8

Buniy, Roman V., and Stephen D. H. Hsu. "Entanglement entropy, black holes and holography." Physics Letters B 644, no. 1 (January 2007): 72–76. http://dx.doi.org/10.1016/j.physletb.2006.10.061.

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9

Colafranceschi, Eugenia, and Gerardo Adesso. "Holographic entanglement in spin network states: A focused review." AVS Quantum Science 4, no. 2 (June 2022): 025901. http://dx.doi.org/10.1116/5.0087122.

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Анотація:

In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to a quantum information theory, such as entanglement, and constitutive features of gravity, like holography. Developing and promoting these connections from the conceptual to the operational level unlock access to a powerful set of tools which can be pivotal toward the formulation of a consistent theory of quantum gravity. Here, we review recent progress on the role and applications of quantum informational methods, in particular tensor networks, for quantum gravity models. We focus on spin network states dual to finite regions of space, represented as entanglement graphs in the group field theory approach to quantum gravity, and illustrate how techniques from random tensor networks can be exploited to investigate their holographic properties. In particular, spin network states can be interpreted as maps from bulk to boundary, whose holographic behavior increases with the inhomogeneity of their geometric data (up to becoming proper quantum channels). The entanglement entropy of boundary states, which are obtained by feeding such maps with suitable bulk states, is then proved to follow a bulk area law with corrections due to the entanglement of the bulk state. We further review how exceeding a certain threshold of bulk entanglement leads to the emergence of a black hole-like region, revealing intriguing perspectives for quantum cosmology.

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10

Jang, Dongmin, Yoonbai Kim, O.-Kab Kwon, and D. D. Tolla. "Exact Holography of Massive M2-brane Theories and Entanglement Entropy." EPJ Web of Conferences 168 (2018): 07002. http://dx.doi.org/10.1051/epjconf/201816807002.

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We test the gauge/gravity duality between the N = 6 mass-deformed ABJM theory with Uk(N) × U-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(4)=ℤk × SO(4)=ℤk isometry. Our analysis is based on the evaluation of vacuum expectation values of chiral primary operators from the supersymmetric vacua of mass-deformed ABJM theory and from the implementation of Kaluza-Klein (KK) holography to the LLM geometries. We focus on the chiral primary operator (CPO) with conformal dimension Δ = 1. The non-vanishing vacuum expectation value (vev) implies the breaking of conformal symmetry. In that case, we show that the variation of the holographic entanglement entropy (HEE) from it’s value in the CFT, is related to the non-vanishing one-point function due to the relevant deformation as well as the source field. Applying Ryu Takayanagi’s HEE conjecture to the 4-dimensional gravity solutions, which are obtained from the KK reduction of the 11-dimensional LLM solutions, we calculate the variation of the HEE. We show how the vev and the value of the source field determine the HEE.

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11

May, Alex. "Complexity and entanglement in non-local computation and holography." Quantum 6 (November 28, 2022): 864. http://dx.doi.org/10.22331/q-2022-11-28-864.

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Does gravity constrain computation? We study this question using the AdS/CFT correspondence, where computation in the presence of gravity can be related to non-gravitational physics in the boundary theory. In AdS/CFT, computations which happen locally in the bulk are implemented in a particular non-local form in the boundary, which in general requires distributed entanglement. In more detail, we recall that for a large class of bulk subregions the area of a surface called the ridge is equal to the mutual information available in the boundary to perform the computation non-locally. We then argue the complexity of the local operation controls the amount of entanglement needed to implement it non-locally, and in particular complexity and entanglement cost are related by a polynomial. If this relationship holds, gravity constrains the complexity of operations within these regions to be polynomial in the area of the ridge.

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12

Liu, Xian-Ming, Hong-Bo Shao, and Xiao-Xiong Zeng. "Van der Waals-Like Phase Transition from Holographic Entanglement Entropy in Lorentz Breaking Massive Gravity." Advances in High Energy Physics 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/6402101.

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Phase transition of AdS black holes in Lorentz breaking massive gravity has been studied in the framework of holography. We find that there is a first-order phase transition (FPT) and second-order phase transition (SPT) both in Bekenstein-Hawking entropy- (BHE-) temperature plane and in holographic entanglement entropy- (HEE-) temperature plane. Furthermore, for the FPT, the equal area law is checked and for the SPT, the critical exponent of the heat capacity is also computed. Our results confirm that the phase structure of HEE is similar to that of BHE in Lorentz breaking massive gravity, which implies that HEE and BHE have some potential underlying relationship.

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13

Obregón, O. "Generalized information and entanglement entropy, gravitation and holography." International Journal of Modern Physics A 30, no. 16 (June 9, 2015): 1530039. http://dx.doi.org/10.1142/s0217751x15300392.

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A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

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14

Michalogiorgakis, Georgios. "Entanglement entropy of two dimensional systems and holography." Journal of High Energy Physics 2008, no. 12 (December 16, 2008): 068. http://dx.doi.org/10.1088/1126-6708/2008/12/068.

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15

Jahn, A., M. Gluza, F. Pastawski, and J. Eisert. "Holography and criticality in matchgate tensor networks." Science Advances 5, no. 8 (August 2019): eaaw0092. http://dx.doi.org/10.1126/sciadv.aaw0092.

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The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand these bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1 + 1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multiscale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error–correcting codes and tensor networks. This work is expected to stimulate a more comprehensive study of tensor network models capturing bulk-boundary correspondences.

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16

Jahnke, Viktor. "Recent Developments in the Holographic Description of Quantum Chaos." Advances in High Energy Physics 2019 (March 26, 2019): 1–18. http://dx.doi.org/10.1155/2019/9632708.

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We review recent developments encompassing the description of quantum chaos in holography. We discuss the characterization of quantum chaos based on the late time vanishing of out-of-time-order correlators and explain how this is realized in the dual gravitational description. We also review the connections of chaos with the spreading of quantum entanglement and diffusion phenomena.

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17

Geng, Hao. "Non-local entanglement and fast scrambling in de-Sitter holography." Annals of Physics 426 (March 2021): 168402. http://dx.doi.org/10.1016/j.aop.2021.168402.

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18

Chen, Chong-Bin, and Fu-Wen Shu. "Towards a Fisher-Information Description of Complexity in de Sitter Universe." Universe 5, no. 12 (November 29, 2019): 221. http://dx.doi.org/10.3390/universe5120221.

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Recent developments on holography and quantum information physics suggest that quantum information theory has come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still unknown. Here, we show that some concepts in quantum information theory have cosmological descriptions. Particularly, we show that the complexity of a tensor network can be regarded as a Fisher information measure (FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for f ( R ) gravity, whose FIM exhibits the same features of a recent proposed L n norm complexity.

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19

Basu, Debarshi, Ashish Chandra, Vinayak Raj, and Gautam Sengupta. "Entanglement wedge in flat holography and entanglement negativity." SciPost Physics Core 5, no. 1 (March 15, 2022). http://dx.doi.org/10.21468/scipostphyscore.5.1.013.

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We establish a construction for the entanglement wedge in asymptotically flat bulk geometries for subsystems in dual (1+1)-dimensional Galilean conformal field theories in the context of flat space holography. In this connection we propose a definition for the bulk entanglement wedge cross section for bipartite states of such dual non relativistic conformal field theories. Utilizing our construction for the entanglement wedge cross section we compute the entanglement negativity for such bipartite states through the generalization of an earlier proposal, in the context of the usual AdS/CFT scenario, to flat space holography. The entanglement negativity obtained from our construction exactly reproduces earlier holographic results and match with the corresponding field theory replica technique results in the large central charge limit.

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20

Hernández-Cuenca, Sergio, Veronika E. Hubeny, and Massimiliano Rota. "The holographic entropy cone from marginal independence." Journal of High Energy Physics 2022, no. 9 (September 22, 2022). http://dx.doi.org/10.1007/jhep09(2022)190.

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Abstract The holographic entropy cone characterizes the relations between entanglement entropies for a spatial partitioning of the boundary spacetime of a holographic CFT in any state describing a classical bulk geometry. We argue that the holographic entropy cone, for an arbitrary number of parties, can be reconstructed from more fundamental data determined solely by subadditivity of quantum entropy. We formulate certain conjectures about graph models of holographic entanglement, for which we provide strong evidence, and rigorously prove that they all imply that such a reconstruction is possible. Our conjectures (except only for the weakest) further imply that the necessary data is remarkably simple. In essence, all one needs to know to reconstruct the holographic entropy cone, is a certain subset of the extreme rays of this simpler “subadditivity cone”, namely those which can be realized in holography. This recasting of the bewildering entanglement structure of geometric states into primal building blocks paves the way to distilling the essence of holography for the emergence of a classical bulk spacetime.

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21

Apolo, Luis, Hongliang Jiang, Wei Song, and Yuan Zhong. "Swing surfaces and holographic entanglement beyond AdS/CFT." Journal of High Energy Physics 2020, no. 12 (December 2020). http://dx.doi.org/10.1007/jhep12(2020)064.

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Abstract We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three- dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.

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22

Du, Dong-Hui, Fu-Wen Shu, and Kai-Xin Zhu. "Inequalities of holographic entanglement of purification from bit threads." European Physical Journal C 80, no. 8 (August 2020). http://dx.doi.org/10.1140/epjc/s10052-020-8283-1.

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Abstract There are increasing evidences that quantum information theory has come to play a fundamental role in quantum gravity especially the holography. In this paper, we show some new potential connections between holography and quantum information theory. Particularly, by utilizing the multiflow description of the holographic entanglement of purification (HEoP) defined in relative homology, we obtain several new inequalities of HEoP under a max multiflow configuration. Each inequality derived for HEoP has a corresponding inequality of the holographic entanglement entropy (HEE). This is further confirmed by geometric analysis. In addition, we conjecture that, based on flow considerations, each property of HEE that can be derived from bit threads may have a corresponding property for HEoP that can be derived from bit threads defined in relative homology.

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23

Apolo, Luis, Hongliang Jiang, Wei Song, and Yuan Zhong. "Modular Hamiltonians in flat holography and (W)AdS/WCFT." Journal of High Energy Physics 2020, no. 9 (September 2020). http://dx.doi.org/10.1007/jhep09(2020)033.

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Abstract We study several aspects of holographic entanglement in two models known as flat3/BMSFT and (W)AdS3/WCFT. These are two examples of holography beyond AdS/CFT where the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS3 or AdS3 backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on “modular chaos” introduced recently in the context of the AdS/CFT correspondence.

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24

Basak, Jaydeep Kumar, Himanshu Chourasiya, Vinayak Raj, and Gautam Sengupta. "Odd entanglement entropy in Galilean conformal field theories and flat holography." European Physical Journal C 82, no. 11 (November 20, 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10980-z.

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AbstractThe odd entanglement entropy (OEE) for bipartite states in a class of $$(1+1)$$ ( 1 + 1 ) -dimensional Galilean conformal field theories ($$GCFT_{1+1}$$ G C F T 1 + 1 ) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for $$(2+1)$$ ( 2 + 1 ) -dimensional asymptotically flat geometries dual to the $$GCFT_{1+1}$$ G C F T 1 + 1 in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.

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25

Hu, Peng-Ju, and Rong-Xin Miao. "Effective action, spectrum and first law of wedge holography." Journal of High Energy Physics 2022, no. 3 (March 2022). http://dx.doi.org/10.1007/jhep03(2022)145.

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Abstract In this paper, we study the effective action, the mass spectrum and the first law of entanglement entropy for a novel doubly holographic model called wedge holography. We work out the effective action of quantum gravity on the branes. In the perturbative formulation, it is given by an infinite sum of Pauli-Fierz actions. In the non-perturbative formulation, the effective action is composed of a higher derivative gravity and a matter action. Usually, a higher derivative gravity can be renormalizable but suffers the ghost problem. For our case, since the effective theory on the brane is equivalent to Einstein gravity in the bulk, it must be ghost-free. We notice that the matter action plays an important role in eliminating the ghost. We also provide evidences that the higher derivative gravity on the brane is equivalent to a ghost-free multi-gravity. Besides, we prove that the effective action yields the correct Weyl anomaly. Interestingly, although the effective action on the brane is an infinite tower of higher derivative gravity, the holographic Weyl anomaly is exactly the same as that of Einstein gravity. We also analyze the mass spectrum of wedge holography. Remarkably, there is always a massless mode of gravitons on the end-of-the-world branes in wedge holography. This happens because one imposes Neumann boundary condition on both branes. On the other hand, the massless mode disappears if one imposes Dirichlet boundary condition on one of the branes as in brane world theory and AdS/BCFT. Finally, we verify the first law of entanglement entropy for wedge holography. Interestingly, the massive fluctuations are irrelevant to the first order perturbation of the holographic entanglement entropy. Thus, in many aspects, the effective theory on the brane behaves like massless Einstein gravity.

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26

Antonini, Stefano, Gregory Bentsen, ChunJun Cao, Jonathan Harper, Shao-Kai Jian, and Brian Swingle. "Holographic measurement and bulk teleportation." Journal of High Energy Physics 2022, no. 12 (December 21, 2022). http://dx.doi.org/10.1007/jhep12(2022)124.

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Abstract Holography has taught us that spacetime is emergent and its properties depend on the entanglement structure of the dual theory. In this paper, we describe how changes in the entanglement due to a local projective measurement (LPM) on a subregion A of the boundary theory modify the bulk dual spacetime. We find that LPMs destroy portions of the bulk geometry, yielding post-measurement bulk spacetimes dual to the complementary unmeasured region Ac that are cut off by end-of-the-world branes. Using a bulk calculation in AdS3 and tensor network models of holography (in particular, the HaPPY code and random tensor networks), we show that the portions of the bulk geometry that are preserved after the measurement depend on the size of A and the state we project onto. The post-measurement bulk dual to Ac includes regions that were originally part of the entanglement wedge of A prior to measurement. This suggests that LPMs performed on a boundary subregion A teleport part of the bulk information originally encoded in A into the complementary region Ac. In semiclassical holography an arbitrary amount of bulk information can be teleported in this way, while in tensor network models the teleported information is upper-bounded by the amount of entanglement shared between A and Ac due to finite-N effects. When A is the union of two disjoint subregions, the measurement triggers an entangled/disentangled phase transition between the remaining two unmeasured subregions, corresponding to a connected/disconnected phase transition in the bulk description. Our results shed new light on the effects of measurement on the entanglement structure of holographic theories and give insight on how bulk information can be manipulated from the boundary theory. They could also represent a first step towards a holographic description of measurement-induced phase transitions.

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27

Kudler-Flam, Jonah, Vladimir Narovlansky, and Shinsei Ryu. "Negativity spectra in random tensor networks and holography." Journal of High Energy Physics 2022, no. 2 (February 2022). http://dx.doi.org/10.1007/jhep02(2022)076.

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Abstract Negativity is a measure of entanglement that can be used both in pure and mixed states. The negativity spectrum is the spectrum of eigenvalues of the partially transposed density matrix, and characterizes the degree and “phase” of entanglement. For pure states, it is simply determined by the entanglement spectrum. We use a diagrammatic method complemented by a modification of the Ford-Fulkerson algorithm to find the negativity spectrum in general random tensor networks with large bond dimensions. In holography, these describe the entanglement of fixed-area states. It was found that many fixed-area states have a negativity spectrum given by a semi-circle. More generally, we find new negativity spectra that appear in random tensor networks, as well as in phase transitions in holographic states, wormholes, and holographic states with bulk matter. The smallest random tensor network is the same as a micro-canonical version of Jackiw-Teitelboim (JT) gravity decorated with end-of-the-world branes. We consider the semi-classical negativity of Hawking radiation and find that contributions from islands should be included. We verify this in the JT gravity model, showing the Euclidean wormhole origin of these contributions.

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28

Swingle, Brian. "Entanglement renormalization and holography." Physical Review D 86, no. 6 (September 5, 2012). http://dx.doi.org/10.1103/physrevd.86.065007.

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29

Karch, Andreas, Zhu-Xi Luo, and Hao-Yu Sun. "Universal relations for holographic interfaces." Journal of High Energy Physics 2021, no. 9 (September 2021). http://dx.doi.org/10.1007/jhep09(2021)172.

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Abstract We study the entanglement entropy in 1+1 dimensional conformal field theories in the presence of interfaces from a holographic perspective. Compared with the well-known case of boundary conformal field theories, interfaces allow for several interesting new observables. Depending on how the interface is located within the entangling region, the entanglement entropies differ and exhibit surprising new patterns and universal relations. While our analysis is performed within the framework of holography, we expect our results to hold more generally.

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30

Grado-White, Brianna, Donald Marolf, and Sean J. Weinberg. "Radial cutoffs and holographic entanglement." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)009.

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Abstract Tensor networks, $$ T\overline{T} $$ T T ¯ , and broader notions of a holographic principle all motivate the idea that some notion of gravitational holography should persist in the presence of a radial cutoff. But in the absence of time-reflection symmetry, the areas of Hubeny-Rangamani-Takayanagi surfaces anchored to the radial cutoff generally violate strong sub-additivity, even when the associated boundary regions are spacelike separated as defined by both bulk and boundary notions of causality. We thus propose an alternate definition of cutoff-holographic entropy using a restricted maximin prescription anchored to a codimension 2 cutoff surface. For bulk solutions that respect the null energy condition, we show that the resulting areas satisfy SSA, entanglement wedge nesting, and monogamy of mutual information in parallel with cutoff free results in AdS. These results hold even when the cutoff surface fails to be convex.

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31

Harper, Jonathan. "Multipartite entanglement and topology in holography." Journal of High Energy Physics 2021, no. 3 (March 2021). http://dx.doi.org/10.1007/jhep03(2021)116.

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Abstract Starting from the entanglement wedge of a multipartite mixed state we describe a purification procedure which involves the gluing of several copies. The resulting geometry has non-trivial topology and a single oriented boundary for each original boundary region. In the purified geometry the original multipartite entanglement wedge cross section is mapped to a minimal surface of a particular non-trivial homology class. In contrast, each original bipartite entanglement wedge cross section is mapped to the minimal wormhole throat around each boundary. Using the bit thread formalism we show how maximal flows for the bipartite and multipartite entanglement wedge cross section can be glued together to form maximal multiflows in the purified geometry. The defining feature differentiating the flows is given by the existence of threads which cross between different copies of the original entanglement wedge. Together these demonstrate a possible connection between multipartite entanglement and the topology of holographic spacetimes.

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32

Miao, Rong-Xin. "An exact construction of codimension two holography." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)150.

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Abstract Recently, a codimension two holography called wedge holography is proposed as a generalization of AdS/CFT. It is conjectured that a gravitational theory in d + 1 dimensional wedge spacetime is dual to a d − 1 dimensional CFT on the corner of the wedge. In this paper, we give an exact construction of the gravitational solutions for wedge holography from the ones in AdS/CFT. By applying this construction, we prove the equivalence between wedge holography and AdS/CFT for vacuum Einstein gravity, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the same for the two theories. The equivalence to AdS/CFT can be regarded as a “proof” of wedge holography in a certain sense. As an application of this powerful equivalence, we derive easily the holographic Weyl anomaly, holographic Entanglement/Rényi entropy and correlation functions for wedge holography. Besides, we discuss the general solutions of wedge holography and argue that they correspond to the AdS/CFT with suitable matter fields. Interestingly, we notice that the intrinsic Ricci scalar on the brane is always a constant, which depends on the tension. Finally, we generalize the discussions to dS/CFT and flat space holography. Remarkably, we find that AdS/CFT, dS/CFT and flat space holography can be unified in the framework of codimension two holography in asymptotically AdS. Different dualities are distinguished by different types of spacetimes on the brane.

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33

Basu, Debarshi, Ashish Chandra, Himanshu Parihar, and Gautam Sengupta. "Entanglement Negativity in Flat Holography." SciPost Physics 12, no. 2 (February 23, 2022). http://dx.doi.org/10.21468/scipostphys.12.2.074.

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We advance holographic constructions for the entanglement negativity of bipartite states in a class of (1+1)-dimensional Galilean conformal field theories dual to asymptotically flat three dimensional bulk geometries described by Einstein Gravity and Topologically Massive Gravity. The construction involves specific algebraic sums of the lengths of bulk extremal curves homologous to certain combinations of the intervals appropriate to such bipartite states. Our analysis exactly reproduces the corresponding replica technique results in the large central charge limit. We substantiate our construction through a semi classical analysis involving the geometric monodromy technique for the case of two disjoint intervals in such holographic Galilean conformal field theories.

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34

de Boer, Jan, Felix M. Haehl, Michal P. Heller, and Robert C. Myers. "Entanglement, holography and causal diamonds." Journal of High Energy Physics 2016, no. 8 (August 2016). http://dx.doi.org/10.1007/jhep08(2016)162.

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35

Jiang, Hongliang, Wei Song, and Qiang Wen. "Entanglement entropy in flat holography." Journal of High Energy Physics 2017, no. 7 (July 2017). http://dx.doi.org/10.1007/jhep07(2017)142.

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36

Mezei, Márk. "On entanglement spreading from holography." Journal of High Energy Physics 2017, no. 5 (May 2017). http://dx.doi.org/10.1007/jhep05(2017)064.

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37

Kong, Ling-Jun, Yifan Sun, Furong Zhang, Jingfeng Zhang, and Xiangdong Zhang. "High-Dimensional Entanglement-Enabled Holography." Physical Review Letters 130, no. 5 (February 2, 2023). http://dx.doi.org/10.1103/physrevlett.130.053602.

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38

Dong, Xi, Xiao-Liang Qi, and Michael Walter. "Holographic entanglement negativity and replica symmetry breaking." Journal of High Energy Physics 2021, no. 6 (June 2021). http://dx.doi.org/10.1007/jhep06(2021)024.

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Abstract Since the work of Ryu and Takayanagi, deep connections between quantum entanglement and spacetime geometry have been revealed. The negative eigenvalues of the partial transpose of a bipartite density operator is a useful diagnostic of entanglement. In this paper, we discuss the properties of the associated entanglement negativity and its Rényi generalizations in holographic duality. We first review the definition of the Rényi negativities, which contain the familiar logarithmic negativity as a special case. We then study these quantities in the random tensor network model and rigorously derive their large bond dimension asymptotics. Finally, we study entanglement negativity in holographic theories with a gravity dual, where we find that Rényi negativities are often dominated by bulk solutions that break the replica symmetry. From these replica symmetry breaking solutions, we derive general expressions for Rényi negativities and their special limits including the logarithmic negativity. In fixed-area states, these general expressions simplify dramatically and agree precisely with our results in the random tensor network model. This provides a concrete setting for further studying the implications of replica symmetry breaking in holography.

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39

Agón, Cesar A., and Márk Mezei. "Bit threads and the membrane theory of entanglement dynamics." Journal of High Energy Physics 2021, no. 11 (November 2021). http://dx.doi.org/10.1007/jhep11(2021)167.

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Abstract Recently, an effective membrane theory was proposed that describes the “hydrodynamic” regime of the entanglement dynamics for general chaotic systems. Motivated by the new bit threads formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the “hydrodynamic” regime without reference to minimal surfaces or membranes.

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40

Donnelly, William, Elise LePage, Yan-Yan Li, Andre Pereira, and Vasudev Shyam. "Quantum corrections to finite radius holography and holographic entanglement entropy." Journal of High Energy Physics 2020, no. 5 (May 2020). http://dx.doi.org/10.1007/jhep05(2020)006.

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41

Ling, Yi, Peng Liu, Yuxuan Liu, Chao Niu, Zhuo-Yu Xian, and Cheng-Yong Zhang. "Reflected entropy in double holography." Journal of High Energy Physics 2022, no. 2 (February 2022). http://dx.doi.org/10.1007/jhep02(2022)037.

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Abstract Recently, the reflected entropy is proposed in holographic approach to describe the entanglement of a bipartite quantum system in a mixed state, which is identified as the area of the reflected minimal surface inside the entanglement wedge. In this paper, we study the reflected entropy in the doubly holographic setup, which contains the degrees of freedom of quantum matter in the bulk. In this context, we propose a notion of quantum entanglement wedge cross-section, which may describe the reflected entropy with higher-order quantum corrections. We numerically compute the reflected entropy in pure AdS background and black hole background in four dimensions, respectively. In general, the reflected entropy contains the contribution from the geometry on the brane and the contribution from the CFT. We compute their proportion for different Newton constants and find that their behaviors are in agreement with the results based on the semi-classical gravity and the correlation of CFT coupled to the bath CFT.

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42

Chou, Chia-Jui, Bo-Han Lin, Bin Wang, and Yi Yang. "Entanglement entropy inequalities in BCFT by holography." Journal of High Energy Physics 2021, no. 2 (February 2021). http://dx.doi.org/10.1007/jhep02(2021)154.

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Abstract We study entanglement entropy inequalities in boundary conformal field theory (BCFT) by holographic correspondence. By carefully classifying all the configurations for different phases, we prove the strong subadditiviy and the monogamy of mutual information for holographic entanglement entropy in BCFT at both zero and finite temperatures.

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43

Basak, Jaydeep Kumar, Himanshu Chourasiya, Vinayak Raj, and Gautam Sengupta. "Reflected entropy in Galilean conformal field theories and flat holography." European Physical Journal C 82, no. 12 (December 26, 2022). http://dx.doi.org/10.1140/epjc/s10052-022-11129-8.

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AbstractWe obtain the reflected entropy for bipartite states in a class of $$(1+1)$$ ( 1 + 1 ) -dimensional Galilean conformal field theories $$(GCFT_{1+1})$$ ( G C F T 1 + 1 ) through a replica technique. Furthermore we compare our results with the entanglement wedge cross section (EWCS) obtained for the dual (2 + 1) dimensional asymptotically flat geometries in the context of flat holography. We find that our results are consistent with the duality between the reflected entropy and the bulk EWCS for flat holographic scenarios.

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44

Chaturvedi, Pankaj, Vinay Malvimat, and Gautam Sengupta. "Entanglement negativity, holography and black holes." European Physical Journal C 78, no. 6 (June 2018). http://dx.doi.org/10.1140/epjc/s10052-018-5969-8.

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45

Nishioka, Tatsuma. "Entanglement entropy: Holography and renormalization group." Reviews of Modern Physics 90, no. 3 (September 17, 2018). http://dx.doi.org/10.1103/revmodphys.90.035007.

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46

Li, Wei, and Tadashi Takayanagi. "Holography and Entanglement in Flat Spacetime." Physical Review Letters 106, no. 14 (April 5, 2011). http://dx.doi.org/10.1103/physrevlett.106.141301.

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47

Bhattacharyya, Arpan, Apratim Kaviraj, and Aninda Sinha. "Entanglement entropy in higher derivative holography." Journal of High Energy Physics 2013, no. 8 (August 2013). http://dx.doi.org/10.1007/jhep08(2013)012.

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48

Dong, Xi, Eva Silverstein, and Gonzalo Torroba. "De Sitter holography and entanglement entropy." Journal of High Energy Physics 2018, no. 7 (July 2018). http://dx.doi.org/10.1007/jhep07(2018)050.

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49

Cartwright, Casey, and Matthias Kaminski. "Inverted c-functions in thermal states." Journal of High Energy Physics 2022, no. 1 (January 2022). http://dx.doi.org/10.1007/jhep01(2022)161.

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Abstract We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory at strong coupling via holography. Depending on the width of the entanglement strip the entanglement entropy probes energy scales from the ultraviolet to the infrared energy regime of this quantum field theory (QFT) prepared in a given state. From the entanglement entropy, we compute holographic c-functions and demonstrate an inverted c-theorem for them. That is, these c-functions in generic thermal states monotonically increase towards the infrared (IR) energy regime. This is in contrast to the c-functions in vacuum states which decrease along the renormalization group flow towards the IR regime of a renormalizable QFT. Furthermore, in thermal states and in the IR limit, the c-functions behave thermally, growing proportionally to the value of the thermal entropy. The chiral anomaly affects the c-functions more in the IR regime, and its effect is peaked at an intermediate value of the magnetic field at a fixed chemical potential and temperature.

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50

Baiguera, Stefano, Lorenzo Bianchi, Shira Chapman, and Damián A. Galante. "Shape deformations of charged Rényi entropies from holography." Journal of High Energy Physics 2022, no. 6 (June 2022). http://dx.doi.org/10.1007/jhep06(2022)068.

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Abstract Charged and symmetry-resolved Rényi entropies are entanglement measures quantifying the degree of entanglement within different charge sectors of a theory with a conserved global charge. We use holography to determine the dependence of charged Rényi entropies on small shape deformations away from a spherical or planar entangling surface in general dimensions. This dependence is completely characterized by a single coefficient appearing in the two point function of the displacement operator associated with the Rényi defect. We extract this coefficient using its relation to the one point function of the stress tensor in the presence of a deformed entangling surface. This is mapped to a holographic calculation in the background of a deformed charged black hole with hyperbolic horizon. We obtain numerical solutions for different values of the chemical potential and replica number n in various spacetime dimensions, as well as analytic expressions for small chemical potential near n = 1. When the Rényi defect becomes supersymmetric, we demonstrate a conjectured relation between the two point function of the displacement operator and the conformal weight of the twist operator.

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