Condensed matter physics, area laws & LQG?

[atyy]

http://arxiv.org/abs/1408.3203
Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
Netta Engelhardt, Aron C. Wall
(Submitted on 14 Aug 2014)
We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.

 

[marcus]

http://arxiv.org/abs/1408.3705
Deriving the First Law of Black Hole Thermodynamics without Entanglement
William R. Kelly
(Submitted on 16 Aug 2014)
In AdS/CFT, how is the bulk first law realized in the boundary CFT? Recently, Faulkner et al. showed that in certain holographic contexts, the bulk first law has a precise microscopic interpretation as a first law of entanglement entropy in the boundary theory. However, the bulk can also satisfy a first law when the boundary density matrix is pure, i.e. in the absence of entanglement with other degrees of freedom. In this note we argue that the bulk first law should generally be understood in terms of a particular coarse-graining of the boundary theory. We use geons, or single-exterior black holes, as a testing ground for this idea. Our main result is that for a class of small perturbations to these spacetimes the Wald entropy agrees to first order with the one-point entropy, a coarse-grained entropy recently proposed by Kelly and Wall. This result also extends the regime over which the one-point entropy is known to be equal to the causal holographic information of Hubeny and Rangamani.
18 pages, 2 figures

This looked interesting and I thought it might fit in with this biblio thread. W.R.Kelly is a young researchers at Santa Barbara who has co-authored a couple of times with Don Marolf and a couple of times with Aron C. Wall (see atty's preceding post).

This might also be of interest to people following this biblio thread:
http://arxiv.org/abs/1408.3989
Observing Shape in Spacetime
Sean Gryb
(Submitted on 18 Aug 2014)
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms - namely hypersurface deformations - are, in a certain sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of "Shape Observer" that represents a conformal reference frame that is dual to the notion of inertial reference frame in spacetime. We then provide a precise dictionary relating the two notions. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.
23 pages, 3 figures.

 

[atyy]

http://arxiv.org/abs/1408.4770
Holographic Holes and Differential Entropy
Matthew Headrick, Robert C. Myers, Jason Wien
(Submitted on 20 Aug 2014)
Recently, it has been shown by Balasubramanian et al. and Myers et al. that the Bekenstein-Hawking entropy formula evaluated on certain closed surfaces in the bulk of a holographic spacetime has an interpretation as the differential entropy of a particular family of intervals (or strips) in the boundary theory. We first extend this construction to bulk surfaces which vary in time. We then give a general proof of the equality between the gravitational entropy and the differential entropy. This proof applies to a broad class of holographic backgrounds possessing a generalized planar symmetry and to certain classes of higher-curvature theories of gravity. To apply this theorem, one can begin with a bulk surface and determine the appropriate family of boundary intervals by considering extremal surfaces tangent to the given surface in the bulk. Alternatively, one can begin with a family of boundary intervals; as we show, the differential entropy then equals the gravitational entropy of a bulk surface that emerges from the intersection of the neighboring entanglement wedges, in a continuum limit.

 

[atyy]

http://arxiv.org/abs/1408.5179
No Firewalls for Black Holes Entangled with Large Systems
Henry Stoltenberg, Andreas Albrecht
(Submitted on 22 Aug 2014)
We question the idea that firewalls are a typical feature of black holes. We first review the arguments of AMPS favoring firewalls, focusing on entanglements in a simple toy model for a black hole and the Hawking radiation. By introducing a large and inaccessible system (representing perhaps a de Sitter stretched horizon or inaccessible part of a landscape) we show complementarity can be restored and firewalls can be avoided throughout the black hole's evolution. We also argue that under these conditions black holes do not have an "information problem".

 

[atyy]

http://arxiv.org/abs/1408.5589
Derivation of Gravitational Field Equation from Entanglement Entropy
Hiroaki Matsueda
(Submitted on 24 Aug 2014)
In this paper, I am going to reformulate my previous work on emergent general relativity from quantum information metric (arXiv:1310.1831) so that we can relate it with some other results based on the entropy-energy relation. For this purpose, I propose a new equality that the second derivative of the entanglement entropy directly represents the spacetime metric. Then, we derive the Einstein tensor from the metric, and consider the meaning of emergent energy-momentum tensor. I demonstrate an explicite example based on spatially one-dimensional quantum states near criticality. I also comment on close connection of the present approach with the Ryu-Takayanagi formula.

 

[atyy]

http://arxiv.org/abs/1408.6005
A Holographic Approach to Spacetime Entanglement
Jason Wien
An essay presented to the Perimeter Institute for the completion of Perimeter Scholars International and the requirements for the degree of Master of Science
(Submitted on 26 Aug 2014)
Recently it has been proposed that the Bekenstein-Hawking formula for the entropy of spacetime horizons has a larger significance as the leading contribution to the entanglement entropy of general spacetime regions, in the underlying quantum theory [2]. This `spacetime entanglement conjecture' has a holographic realization that equates the entropy formula evaluated on an arbitrary space-like co-dimension two surface with the differential entropy of a particular family of co-dimension two regions on the boundary. The differential entropy can be thought of as a directional derivative of entanglement entropy along a family of surfaces. This holographic relation was first studied in [3] and extended in [4], and it has been proven to hold in Einstein gravity for bulk surfaces with planar symmetry (as well as for certain higher curvature theories) in [4]. In this essay, we review this proof and provide explicit examples of how to build the appropriate family of boundary intervals for a given bulk curve. Conversely, given a family of boundary intervals, we provide a method for constructing the corresponding bulk curve in terms of intersections of entanglement wedge boundaries. We work mainly in three dimensions, and comment on how the constructions extend to higher dimensions.

 

[atyy]

http://arxiv.org/abs/1408.6300
Causality & holographic entanglement entropy
Matthew Headrick, Veronika E. Hubeny, Albion Lawrence, Mukund Rangamani
(Submitted on 27 Aug 2014)
We identify conditions for the entanglement entropy as a function of spatial region to be compatible with causality in an arbitrary relativistic quantum field theory. We then prove that the covariant holographic entanglement entropy prescription (which relates entanglement entropy of a given spatial region on the boundary to the area of a certain extremal surface in the bulk) obeys these conditions, as long as the bulk obeys the null energy condition. While necessary for the validity of the prescription, this consistency requirement is quite nontrivial from the bulk standpoint, and therefore provides important additional evidence for the prescription. In the process, we introduce a codimension-zero bulk region, named the entanglement wedge, naturally associated with the given boundary spatial region. We propose that the entanglement wedge is the most natural bulk region corresponding to the boundary reduced density matrix.

 

[atyy]

http://arxiv.org/abs/1408.6633
Geodesic Distance in Fisher Information Space and Holographic Entropy Formula
Hiroaki Matsueda
(Submitted on 28 Aug 2014)
In this short note, we examine geodesic distance in Fisher information space in which the metric is defined by the entanglement entropy in CFT_(1+1). It is obvious in this case that the geodesic distance at a constant time is a function of the entropy data embedded into the information space. In a special case, the geodesic equation can be solved analytically, and we find that the distance agrees well with the Ryu-Takayanagi formula. Then, we can understand how the distance looks at the embeded quantum information. The result suggests that the Fisher metric is an efficient tool for constructing the holographic spacetime.

 

[friend]

http://arxiv.org/abs/1408.6633
Geodesic Distance in Fisher Information Space and Holographic Entropy Formula

It sounds here as if the author has connected GR to QM. That would be amazing, right?

 

[atyy]

Posted by marcus in his bibliography https://www.physicsforums.com/showpost.php?p=4839015&postcount=2240

http://arxiv.org/abs/1409.0144
Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
Eugenio Bianchi, Tommaso De Lorenzo, Matteo Smerlak
(Submitted on 30 Aug 2014)
We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that (i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, (ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, (iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

 

[atyy]

It sounds here as if the author has connected GR to QM. That would be amazing, right?

Yes, it would be amazing. Here is a slightly earlier paper by Matsueda http://arxiv.org/abs/1408.5589 which proposes a way to extend the results of Blanco et al http://arxiv.org/abs/1305.3182. Blanco's work was important, because it showed how within AdS/CFT which is already a proposal connecting QM and GR, one might understand the thermodynamic derivation of GR by Jacobson.

 

[atyy]

http://arxiv.org/abs/1409.1231
Jerusalem Lectures on Black Holes and Quantum Information
Daniel Harlow
(Submitted on 3 Sep 2014)
In these lectures I give an introduction to the quantum physics of black holes, including recent developments based on quantum information theory such as the firewall paradox and its various cousins. I also give an introduction to holography and the AdS/CFT correspondence, focusing on those aspects which are relevant for the black hole information problem.

 

[atyy]

http://arxiv.org/abs/1409.1603
Non-Unitary Holography
Cumrun Vafa
(Submitted on 4 Sep 2014)
We propose gauge theory/gravity duality involving conformal theories based on U(N+k|k) gauge groups. We show that to all orders in 1/N these non-unitary theories based on supergroups are indistinguishable from the corresponding unitary theories where the gauge group is replaced by U(N). This leads to non-unitary gravity duals which to all orders in 1/N are indistinguishable from their unitary cousins. They are distinguished by operators whose correlation functions differ by O(exp(-aN)). The celebrated type IIB on AdS^5 x S^5 and M-theory on AdS^4 x S^7 fall in this class and thus seem to also admit non-unitary non-perturbative completions. It is tempting to conjecture that this setup may provide a non-unitary model for black hole evaporation.

 

[atyy]

http://arxiv.org/abs/1409.2407
Decorated tensor network renormalization for lattice gauge theories and spin foam models
Bianca Dittrich, Sebastian Mizera, Sebastian Steinhaus
(Submitted on 8 Sep 2014)
Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a challenge for standard tensor network algorithms. We accommodate for such systems by introducing an additional structure decorating the tensor network. This allows to explicitly preserve the gauge symmetry of the system under coarse graining and straightforwardly interpret the fixed point tensors. Using this novel information encoded in the decoration might eventually lead to new methods incorporating both analytical and numerical techniques.

 

[atyy]

http://arxiv.org/abs/1409.3150
Group field theories for all loop quantum gravity
Daniele Oriti, James P. Ryan, Johannes Thürigen
(Submitted on 10 Sep 2014)
Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the GFT formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

http://arxiv.org/abs/1409.3085
A Formulation of Lattice Gauge Theories for Quantum Simulations
Erez Zohar, Michele Burrello
(Submitted on 10 Sep 2014)
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete D3 gauge group, are presented.

 

[atyy]

I'm not entirely sure how this fits in, but one things I've been becoming aware of is that entanglement is relative. The entanglement entropy is absolute, in the sense that it is basis independent. However, here are some discussions that the notion of entanglement is relative.

http://arxiv.org/abs/quant-ph/0206135
Entanglement of photons
S.J. van Enk
(Submitted on 19 Jun 2002)
It is argued that the title of this paper represents a misconception. Contrary to widespread beliefs it is electromagnetic field modes that are "systems'' and can be entangled, not photons. The amount of entanglement in a given state is shown to depend on redefinitions of the modes; we calculate the minimum and maximum over all such redefinitions for several examples.

http://arxiv.org/abs/1302.3509
Universal Separability and Entanglement in Identical Particle Systems
Toshihiko Sasaki, Tsubasa Ichikawa, Izumi Tsutsui
(Submitted on 14 Feb 2013)
Entanglement is known to be a relative notion, defined with respect to the choice of physical observables to be measured (i.e., the measurement setup used). This implies that, in general, the same state can be both separable and entangled for different measurement setups, but this does not exclude the existence of states which are separable (or entangled) for all possible setups. We show that for systems of bosonic particles there indeed exist such universally separable states: they are i.i.d. pure states. In contrast, there is no such state for fermionic systems with a few exceptional cases. We also find that none of the fermionic and bosonic systems admits universally entangled states.

 

[marcus]

http://arxiv.org/abs/1409.8339
All-fermion electrodynamics and fermion number anomaly inflow
S. M. Kravec, John McGreevy, Brian Swingle
(Submitted on 29 Sep 2014)
We demonstrate that 3+1-dimensional quantum electrodynamics with fermionic charges, fermionic monopoles, and fermionic dyons arises at the edge of a 4+1-dimensional gapped state with short-range entanglement. This state cannot be adiabatically connected to a product state, even in the absence of any symmetry. This provides independent evidence for the obstruction found byarXiv:1306.3238 to a 3+1-dimensional short-distance completion of all-fermion electrodynamics. The non-triviality of the bulk is demonstrated by a novel fermion number anomaly.
37 pages, 5 figures
Although I can't reliably tell, this sounded to me as if it might be of interest to you and might fit into the context of this thread. Atyy, let me know if it does't fit and I'll be happy to delete.

 

[atyy]

Although I can't reliably tell, this sounded to me as if it might be of interest to you and might fit into the context of this thread. Atyy, let me know if it does't fit and I'll be happy to delete.

Thanks for posting the Kravec, McGreevy, and Swingle paper! I think it's good to cast the net widely and to post whatever we think is potentially interesting.

 

[atyy]

http://arxiv.org/abs/1410.1540
The Information Theoretic Interpretation of the Length of a Curve
Bartlomiej Czech, Patrick Hayden, Nima Lashkari, Brian Swingle
(Submitted on 6 Oct 2014)
In the context of holographic duality with AdS3 asymptotics, the Ryu-Takayanagi formula states that the entanglement entropy of a subregion is given by the length of a certain bulk geodesic. The entanglement entropy can be operationalized as the entanglement cost necessary to transmit the state of the subregion from one party to another while preserving all correlations with a reference party. The question then arises as to whether the lengths of other bulk curves can be interpreted as entanglement costs for some other information theoretic tasks. Building on recent results showing that the length of more general bulk curves is computed by the differential entropy, we introduce a new task called constrained state merging, whereby the state of the boundary subregion must be transmitted using operations restricted in location and scale in a way determined by the geometry of the bulk curve. Our main result is that the cost to transmit the state of a subregion under the conditions of constrained state merging is given by the differential entropy and hence the signed length of the corresponding bulk curve. When the cost is negative, constrained state merging distills entanglement rather than consuming it. This demonstration has two parts: first, we exhibit a protocol whose cost is the length of the curve and second, we prove that this protocol is optimal in that it uses the minimum amount of entanglement. In order to complete the proof, we additionally demonstrate that single-shot smooth conditional entropies for intervals in 1+1-dimensional conformal field theories with large central charge are well approximated by their von Neumann counterparts. We also revisit the relationship between the differential entropy and the maximum entropy among locally consistent density operators, demonstrating large quantitative discrepancy between the two quantities in conformal field theories.

 

[atyy]

http://arxiv.org/abs/1410.2870
Unravelling Holographic Entanglement Entropy in Higher Spin Theories
Alejandra Castro, Eva Llabrés
(Submitted on 10 Oct 2014)
There are two proposals that compute holographic entanglement entropy in AdS3 higher spin theories based on SL(N,R) Chern-Simons theory. We show explicitly that these two proposals are equivalent. We also designed two methods that solve systematically the equations for arbitrary N. For finite charge backgrounds in AdS3, we find exact agreement between our expressions and the short interval correction of the entanglement entropy for an excited state in a CFT2.

 

[atyy]

http://arxiv.org/abs/1410.7773
Large-N transitions of the connectivity index
Francesco Aprile, Vasilis Niarchos
(Submitted on 28 Oct 2014)
The connectivity index, defined as the number of decoupled components of a quantum system, can change under deformations of the Hamiltonian or during the dynamical change of the system under renormalization group flow. Such changes signal a rearrangement of correlations of different degrees of freedom across spacetime and field theory space. In this paper we quantify such processes by studying the behavior of entanglement entropy, relative quantum entropy and quantum mutual information in a specific example: the RG flow in the Coulomb branch of large-N superconformal field theories. We argue that in this context there is an interesting sharp large-N transition in the middle of the RG flow from a non-separable phase of the Higgsed UV gauge theory to a separable phase of deformed decoupled CFTs in the IR. The entanglement entropy on a sphere with radius ℓ detects this transition via the formation of a separatrix on the co-dimension-two Ryu-Takayanagi surface in multi-centered brane geometries above a critical value of ℓ. Other measures of entanglement and separability based on the relative quantum entropy detect a transition to a phase where they vanish identically. From the IR point of view the effect is closely related to the resummation of an infinite set of irrelevant multi-trace interactions.

 

[atyy]

http://arxiv.org/abs/1405.6394
Finite N and the failure of bulk locality: Black holes in AdS/CFT
Daniel Kabat, Gilad Lifschytz
(Submitted on 25 May 2014 (v1), last revised 20 Jul 2014 (this version, v2))
We consider bulk quantum fields in AdS/CFT in the background of an eternal black hole. We show that for black holes with finite entropy, correlation functions of semiclassical bulk operators close to the horizon deviate from their semiclassical value and are ill-defined inside the horizon. This is due to the large-time behavior of correlators in a unitary CFT, and means the region near and inside the horizon receives corrections. We give a prescription for modifying the definition of a bulk field in a black hole background, such that one can still define operators that mimic the inside of the horizon, but at the price of violating microcausality. For supergravity fields we find that commutators at spacelike separation generically ~ exp(-S/2). Similar results hold for stable black holes that form in collapse. The general lesson may be that a small amount of non-locality, even over arbitrarily large spacelike distances, is an essential aspect of non-perturbative quantum gravity.

http://arxiv.org/abs/1411.0690
Entanglement is not Enough
Leonard Susskind
(Submitted on 3 Nov 2014)
This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity. I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.

 

[atyy]

Reading Susskind's "Entanglenent is not enough", I see he and Stanford discussed tensor networks in these two papers:

http://arxiv.org/abs/1406.2678
Complexity and Shock Wave Geometries
Douglas Stanford, Leonard Susskind
(Submitted on 10 Jun 2014 (v1), last revised 12 Jun 2014 (this version, v2))
In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state. Our refinement states that the complexity is proportional to the spatial volume of the ERB. More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by GNlAdS. We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions. We find detailed agreement.

Edit: I deleted one reference, because I cut and pasted wrongly. The right paper is in the next post. Thanks, marcus!

 

[marcus]

Belongs with previous post:
http://arxiv.org/abs/1409.8180
Localized shocks
Daniel A. Roberts, Douglas Stanford, Leonard Susskind
(Submitted on 29 Sep 2014)
We study products of precursors of spatially local operators, W_xn(t_n)...W_x1(t₁), where W_x(t)=e^−iHtW_xe^iHt. Using chaotic spin-chain numerics and gauge/gravity duality, we show that a single precursor fills a spatial region that grows linearly in t. In a lattice system, products of such operators can be represented using tensor networks. In gauge/gravity duality, they are related to Einstein-Rosen bridges supported by localized shock waves. We find a geometrical correspondence between these two descriptions, generalizing earlier work in the spatially homogeneous case.
23 pages plus appendices, 11 figures

 

[atyy]

The 2015 New Horizons in Physics Prizes

Sean Hartnoll, Stanford University, for applying holographic methods to obtain remarkable new insights into strongly interacting quantum matter.

Philip C. Schuster and Natalia Toro, Perimeter Institute, for pioneering the “simplified models” framework for new physics searches at the Large Hadron Collider, as well as spearheading new experimental searches for dark sectors using high-intensity electron beams.

Horacio Casini and Marina Huerta, CONICET and Instituto Balseiro, Universidad Nacional de Cuyo, Shinsei Ryu, University of Illinois at Urbana-Champaign, and Tadashi Takayanagi, Kyoto University, for fundamental ideas about entropy in quantum field theory and quantum gravity.

 

[atyy]

http://arxiv.org/abs/1411.7041
Bulk Locality and Quantum Error Correction in AdS/CFT
Ahmed Almheiri, Xi Dong, Daniel Harlow
(Submitted on 25 Nov 2014)
We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

 

[atyy]

http://simons.berkeley.edu/talks/brian-swingle-2014-04-22
Einstein's Equations Starting from Qubits
Brian Swingle, Harvard University

Part of the Tensor Networks and Simulations workshop, with lots of other good stuff at http://simons.berkeley.edu/workshops/schedule/81.

 

[marcus]

...good stuff at http://simons.berkeley.edu/workshops/schedule/81.
Including talks by Guifre Vidal and Xiao-Gang Wen : ^)

 

[atyy]

...good stuff at http://simons.berkeley.edu/workshops/schedule/81.
Including talks by Guifre Vidal and Xiao-Gang Wen : ^)

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

 

[inflector]

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

Check out his paper with Ashvin Vishwanath of the same title from January:

http://arxiv.org/abs/1401.3736

'Gauging' time reversal symmetry in tensor network states
Xie Chen, Ashvin Vishwanath
Abstract:

It is well know that unitary symmetries can be `gauged', i.e. defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an anti-unitary symmetry. Here we discuss a route to gauging time reversal symmetry that applies to gapped quantum ground states. We show how time reversal can be applied locally and also describe time reversal symmetry twists which act as gauge fluxes through nontrivial loops in the system. The procedure is based on the tensor network representation of quantum states which provides a notion of locality for the wave function coefficient. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain symmetry protected topological phases in D=1,2 are readily extracted using these ideas and also discuss how they help capture a subtle distinction between time reversal symmetric Z2 gauge theories.​

 

[marcus]

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

She was a postdoc for 2 years at Berkeley in Ashvin Vishwanath's group:
https://sites.google.com/site/ashvinvish/Home/people
and in July 2014 moved to Caltech to take a faculty position. Bright young person in what seems like a good field of research to be in. A kind of combination of Quantum Information theory and Condensed Matter?
Here's a Caltech blurb about her joining the faculty
http://www.caltech.edu/news/quantum-information-meets-condensed-matter-inside-mind-xie-chen-43439
She got her PhD at MIT, I vaguely remember her co-authoring with Xiao-Gang Wen, maybe he was her advisor.

 

[atyy]

At the end of his talk, Physics Monkey argues that one can actually get the nonlinear Einstein equations (he just mentions it without much detail, the talk is mainly about the linearized equation). I think so far the published papers only say how to get the linearized Einstein equations, so that should be an interesting paper to wait for.

 

[marcus]

At the end of his talk, Physics Monkey argues that one can actually get the nonlinear Einstein equations (he just mentions it without much detail, the talk is mainly about the linearized equation). I think so far the published papers only say how to get the linearized Einstein equations, so that should be an interesting paper to wait for.

You already gave the link to Physics Monkey's talk, but we've turned a page so I'll bring it forward:
http://simons.berkeley.edu/talks/brian-swingle-2014-04-22
Einstein's Equations Starting from Qubits
Brian Swingle, Harvard University

I was not aware of published papers deriving linearized GR, so one of us should probably post links here as a convenience for anyone who wants to check out what versions of Einstein's equations are being derived from what. It's all pretty interesting! You may recall the LQG paper by Chirco et al which derives the full non-linear Einstein GR equation from quantum gravity degrees of freedom---by showing that it can indeed be viewed as a thermodynamic equation of state (as Jacobson already proved in 1995), but of specific microscopic QG (rather than unknown "hidden" variables, as Jacobson originally suggested).
http://arxiv.org/abs/1401.5262
Spacetime thermodynamics without hidden degrees of freedom
Goffredo Chirco, Hal M. Haggard, Aldo Riello, Carlo Rovelli
(Submitted on 21 Jan 2014)
A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.
12 pages, 1 figure

 

[atyy]

http://arxiv.org/abs/1412.0687
Entanglement entropy in three dimensional gravity
Henry Maxfield
(Submitted on 1 Dec 2014)
The Ryu-Takayanagi and covariant Hubeny-Rangamani-Takayanagi proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotients of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.

 

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http://arxiv.org/abs/1412.1879
Tomography from Entanglement
Jennifer Lin, Matilde Marcolli, Hirosi Ooguri, Bogdan Stoica
(Submitted on 5 Dec 2014)
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory, follow from positivity conditions on the bulk matter energy density. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

http://arxiv.org/abs/1412.1895
Entanglement entropy of electromagnetic edge modes
William Donnelly, Aron C. Wall
(Submitted on 5 Dec 2014)
The vacuum entanglement entropy of Maxwell theory, when evaluated by standard methods, contains an unexpected term with no known statistical interpretation. We resolve this two-decades old puzzle by showing that this term is the entanglement entropy of edge modes: classical solutions determined by the electric field normal to the entangling surface. We explain how the heat kernel regularization applied to this term leads to the negative divergent expression found by Kabat. This calculation also resolves a recent puzzle concerning the logarithmic divergences of gauge fields in 3+1 dimensions.