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Quantum Information in Quantum Gravity II

Conference Date: 
Monday, August 17, 2015 (All day) to Friday, August 21, 2015 (All day)
Scientific Areas: 
Quantum Fields and Strings
Quantum Gravity
Quantum Information

 

This workshop is dedicated to the memory of Jacob Bekenstein (May 1, 1947 - August 16, 2015.)  
A pathfinder who never stopped looking for new horizons,

This is the second in a series of workshops aimed at facilitating discussion on applying information theoretic concepts to tackle quantum gravity conundrums. The first workshop was held at the University of British Columbia in August 2014.  In recent years, we have seen an increasing interplay between the quantum information and the string/quantum gravity communities and we aim to facilitate further interaction in this front. We plan to have a a few talks per day with lots of time for discussions.
 
Registration for this workshop is now closed.
 
We also encourage interested researchers to apply for the Mathematica Summer School on Entanglement, which will be hosted at Perimeter Institute in the following week (August 24-29, 2015).
 
Sponsorship for this workshop has been provided by:

 

  • Ning Bao, California Institute of Technology
  • Alessio Belenchia, SISSA
  • Adam Brown, Stanford University
  • Horacio Casini, Centro Atomico Bariloche
  • Aidan Chatwin-Davies, California Institute of Technology
  • Bartek Czech, Stanford University
  • Bianca Dittrich, Perimeter Institute
  • William Donnelly, University of California, Santa Barbara
  • Glen Evenbly, California Institute of Technology
  • Thomas Faulkner, University of Illinois
  • Jutho Haegeman, University of Ghent
  • Matthew Headrick, Brandeis University
  • Michal Heller, Perimeter Institute
  • Veronika Hubeny, Durham University
  • Ted Jacobson, University of Maryland
  • Nima Lashkari, Massachusetts Institute of Technology
  • Aitor Lewkowycz, Princeton University
  • Mark Mezei, Princeton University
  • Jonathan Oppenheim, University College London
  • Fernando Pastawski, California Institute of Technology
  • Xiao-Liang Qi, Stanford University
  • Mukund Rangamani, University of Durham
  • Subir Sachdev, Harvard University
  • Grant Salton, Stanford University
  • James Sully, Stanford University
  • Tadashi Takayanagi, Yukawa Institute for Theoretical Physics, Kyoto University
  • Aron Wall, Institute for Advanced Study
  • Beni Yoshida, Californai Institute of Technology
  • Aysha Abdel-Aziz, Perimeter Institute
  • Nima Afkhami-Jeddi, Cornell University 
  • Ahmed Almheiri, Stanford University
  • Ning Bao, California Institute of Technology
  • Alessio Belenchia, SISSA
  • Jake Bian, University of British Columbia
  • Adam Brown, Stanford University
  • Chris Brust, Perimeter Institute
  • Pawel Caputa, Nordita
  • Horacio Casini, Centro Atomico Bariloche
  • Aidan Chatwin-Davies, California Institute of Technology
  • Wissam Chemissany, Stanford University
  • Linqing Chen, Perimeter Institute
  • Jesse Cresswell, University of Toronto
  • Bartek Czech, Stanford University
  • Arundhati Dasgupta, University of Lethbridge
  • Clement Declamp, Perimeter Institute
  • Bianca Dittrich, Perimeter Institute
  • William Donnelly, University of California, Santa Barbara
  • Netta EngelhardtUniversity of California, Santa Barbara
  • Glen Evenbly, California Institute of Technology
  • Thomas Faulkner, University of Illinois
  • Damian Galante, Perimeter Institute & University of Western Ontario
  • Henrique Gomes, Perimeter Institute
  • Jutho Haegeman, University of Ghent
  • Matthew Headrick, Brandeis University
  • Michal Heller, Perimeter Institute
  • Veronika Hubeny, Durham University
  • Nick Hunter-Jones, California Institute of Technology
  • Ted Jacobson, University of Maryland
  • Ian Jardine, University of Toronto
  • Achim Kempf, Perimeter Institute & University of Waterloo
  • Lampros Lamprou, Stanford University
  • Nima Lashkari, Massachusetts Institute of Technology
  • Aitor Lewkowycz, Princeton University
  • Sam McCandlish, Stanford University
  • Roger Melko, Perimeter Institute & University of Waterloo
  • Mark Mezei, Princeton University
  • Ashley Milsted, Leibniz Universität Hannover
  • Masamichi Miyaji, Yukawa Institute for Theoretical Physics
  • Tokiro Numasawa, Yukawa Institute for Theoretical Physics
  • Jonathan Oppenheim, University College London
  • Fernando Pastawski, California Institute of Technology
  • Amanda Peet, University of Toronto
  • Xiao-Liang Qi, Stanford University
  • Mukund Rangamani, University of Durham
  • Benni Reznik, Tel Aviv University
  • Simon Ross, Durham University
  • Grant Salton, Stanford University
  • Barak Shoshany, Perimeter Institute
  • Vasudev Shyam, Perimeter Institute
  • James Sully, Stanford University
  • Tadashi TakayanagiYukawa Institute for Theoretical Physics, Kyoto University
  • Frank Verstraete, University of Ghent
  • Aron Wall, Institute for Advanced Study
  • Yasaman Yazdi, Perimeter Institute
  • Beni YoshidaCaltifornia Institute of Technology
  • Ida ZadehBrandeis University
  • Claire Zukowski, Perimeter Institute
  • Nosiphiwo Zwane, Perimeter Institute

Monday, August 17, 2015

Time

Event

Location

8:30 – 9:00am

Registration

Reception

9:00 – 9:05am

Welcome and Opening Remarks

Bob Room

 

Chair 
Rob Myers,
Perimeter Institute

Bob Room

9:05 – 10:00am

Tadashi Takayanagi, Yukawa Institute for Theoretical Physics,
Kyoto University
Gravity Dual of Quantum Information Metric

Bob Room

10:00 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Matthew Headrick, Brandeis University
A new perspective on holographic entanglement

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

 

Chair
Amanda Peet,
University of Toronto

Bob Room

2:00 – 3:00pm

Thomas Faulkner, University of Illinois
Universal holographic description of CFT entanglement entropy

Bob Room

3:00 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Veronika Hubeny, Durham University
Geometric Constructs in AdS/CFT

Bob Room

5:00 – 5:30pm

Jonathan Oppenheim, University College London
Do Black Holes Create Polyamory

Bob Room

 

Tuesday,August 18, 2015

Time

Event

Location

 

Chair
Guifre Vidal,
Perimeter Institute

 

9:00 – 10:00am

Glen Evenbly, California Institute of Technology
Tensor Network Renormalization and the MERA

Bob Room

10:00 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Jutho Haegemann, University of Ghent
Entanglement renormalization for quantum fields

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

 

Chair
Benni Reznik,
Tel Aviv University

Bob Room

2:00 – 3:00pm

Fernando Pastawski, California Institute of Technology
Holographic quantum error-correcting codes: 
Toy models for the bulk/boundary correspondence

Bob Room

3:00 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 4:30pm

Ning Bao, California Institute of Technology
The Holographic Entropy Cone

Bob Room

4:30 – 5:00pm

Mark Mezei, Princeton University
Spread of entanglement and causality

Bob Room

5:00 – 5:30pm

Beni Yoshida, California Institute of Technology
Order parameter for chaos

Bob Room

 

Wednesday, August 19, 2015

Time

Event

Location

 

Chair
Arundhati Dasgupta,
University of Lethbridge

Bob Room

9:00 – 10:00am

Horacio Casini, Centro Atomico Bariloche
Area terms in entanglement entropy

Bob Room

10:00 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Aron Wall, Institute for Advanced Study
Entropic Focussing

Bob Room

12:00 – 12:10pm

Conference Photo

TBA

12:10 – 2:00pm

Lunch

Bistro – 2nd Floor

 

Chair
Mark van Raamsdonk, University of British Columbia

Bob Room

2:00 – 3:00pm

Ted Jacobson, University of Maryland
Einstein's equation from maximal entropy of vacuum entanglement

Bob Room

3:00 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 - 4:30pm

Aitor Lewkowycz, Princeton University
Towards a derivation of covariant holographic entanglement

 

4:30 – 5:00pm

Gong Show:
Alessio Belenchia, SISSA
Analogue Gravity
Aidan Chatwin-Davies, California Institute of Technology
Consistency Conditions for an AdSMERA Correspondence
Grant Salton, Stanford University
Replicating Quantum Information in Spacetime

Bob Room

5:00 – 5:30pm

Poster Session Viewing:
Netta Englehardt, University of California, Santa Barbara
Damian Galante, Perimeter Institute
Lampros Lamprou, Stanford University
Sam McCandlish, Stanford University
Masamichi Miyaji, Kyoto University
Tokiro Numasawa, Kyoto University

Atrium

6:00pm onwards

BBQ

Bistro – 1st Floor

 

Thursday, August 20, 2015

Time

Event

Location

 

Chair
Veronika Hubeny, Durham University

Bob Room

9:00 – 10:00am

James Sully, Stanford University
What to Expect in Kinematic Space

Bob Room

10:00 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Bartek Czech, Stanford University
Quotients of MERA

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

 

Chair
Matthew Headrick, Brandeis University

Bob Room

2:00 – 3:00pm

Xiao-Liang Qi, Stanford University
Holographic mapping, quantum error correction code
and sub-AdS locality

Bob Room

3:00 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 4:30pm

Michal Heller, Perimeter Institute
AdS/CFT Holography Integrability

Bob Room

4:30 – 5:00pm

William Donnelly, University of California, Santa Barbara
Diffeomorphism-invariant observables and nonlocality

Bob Room

5:00 – 5:30pm

Subir Sachdev, Harvard University
Bekenstein-Hawking entropy and strange metals

Bob Room

 

Friday, August 21 2015

Time

Event

Location

 

Chair
Simon Ross, Durham University

Bob Room

9:00 – 10:00am

Adam Brown, Stanford University
Wormholes and Complexity

Bob Room

10:00 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Nima Lashkari, Massachusetts Institute of Technology
Quantum Fisher metric in field theory and gravity

Bob Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

 

Chair
Frank Verstraete, University of Ghent

 

2:00 – 3:00pm

Bianca Dittrich, Perimeter Institute
3D Holography:  from discretum to continuum

Bob Room

3:00 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Mukund Rangamani, University of Durham
Positivity, negativity, entanglement, and holography

Bob Room

 

 

 

Ning Bao, California Institute of Technology

The Holographic Entropy Cone

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory. 

Alessio Belenchia, SISSA

Analogue Gravity

Adam Brown, Stanford University

Wormholes and Complexity

I will discuss the connection between wormholes, action, computation and complexity.

Horacio Casini, Centro Atomico Bariloche

Area terms in entanglement entropy

We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the Adler-Zee  sum rule for the renormalization of the Newton constant in terms of correlator of traces of the stress tensor. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We check the sum rule holographicaly. We also discuss an application to the F-theorem. 

Aidan Chatwin-Davies, California Institute of Technology

Consistency Conditions for an AdSMERA Correspondence

Bartek Czech, Standford University

Quotients of MERA

Bianca Dittrich, Perimeter Institute

3D Holography:  from discretum to continuum

William Donnelly, University of California, Santa Barbara

Diffeomorphism-invariant observables and nonlocality

In a theory of gravity, observables must be diffeomorphism-invariant. Such observables are nonlocal, in contrast with the usual formulation of local quantum field theory. Working to leading order in Newtons constant G, I'll describe a construction of diffeomorphism-invariant observables for a scalar field coupled to gravity that closely parallels an analogous construction for charged particles in electrodynamics. These observables acting on the vacuum create scalar particles together with their (linearized) gravitational dressing. The commutator of two such spacelike-separated observables is nonvanishing at order G, and is related to the gravitational potential between two masses.

Based on arXiv:1507.07921 with Steve Giddings.

Glen EvenblyCalifornia Institute of Technology

Tensor Network Renormalization and the MERA

I describe a class of non-perturbative renormalization group (RG) transformations which, when applied to the (discrete time) Euclidean path integrals of a quantum systems on the lattice, can give results consistent with conformal transformations of quantum field theories. In particular, this class of transformation, which we call Tensor Network Renormalization (TNR), is shown to generate a scale-invariant RG flow for quantum systems at a critical point. Applications of TNR towards study of quantum critical systems, and its relationship to the multi-scale-entanglement renormalization ansatz (MERA) for ground and thermal states of quantum systems, will be discussed.

Thomas Faulkner, University of Illinois

Universal holographic description of CFT entanglement entropy

The Ryu-Takayanagi proposal (and generalizations) for holographic entanglement makes predictions for geometric CFT entanglement entropy (EE) that continue to hold for any CFT, regardless of existence of large-N limit or strong coupling.  We establish this using a direct field theory calculation, thus providing a non-trivial check of the holographic proposal. This universality emerges for small perturbations of the EE of a ball shaped region. Einstein’s equations arise from the field theory calculation as a way to efficiently encode this perturbative CFT entanglement holographically in the geometry of a dual space-time. 

Jutho Haegeman, University of Ghent

Entanglement renormalization for quantum fields 

The Multiscale Entanglement Renormalization Ansatz has proven to capture the ground state properties of strongly correlated quantum lattice systems, both in gapped regimes and at critical points, and realizes a lattice version of the holographic principle. In this talk, I will review a construction of entanglement renormalization that applies in the continuum (i.e. to quantum fields) and discuss several aspects such as the renormalization group equation and scaling exponents, illustrated using free field theories as example

Matthew HeadrickBrandeis University

A new perspective on holographic entanglement

We will present a reformulation of the Ryu-Takayanagi holographic entanglement entropy formula which does not involve the areas of surfaces. The reformulation leads to a picture of entanglement entropy of boundary regions being carried by Planck-thickness "bit threads" in the bulk. We will argue that this picture resolves a number of conceptual difficulties surrounding the RT formula.

Michal Heller, Perimeter Institute

AdS/CFT Holography Integrability

Veronika Hubeny, Durham University

Geometric Constructs in AdS/CFT

Ted JacobsonUniversity of Maryland

Einstein's equation from maximal entropy of vacuum entanglement

If entanglement entropy in a small geodesic ball is maximized at fixed volume in the vacuum, then it should be stationary under variation to a nearby state. I will show that this stationarity condition is equivalent to the semiclassical Einstein equation. If the matter QFT is not conformal, then the derivation requires a further assumption about QFT, whose validity is currently under investigation. [Based on http://arxiv.org/abs/1505.04753]

Nima LashkariMassachusetts Institute of Technology

Quantum Fisher metric in field theory and gravity

In the first part of this talk, we discuss a generalized replica trick that is based on replica symmetry breaking partitions. This allows us compute the modular Hamiltonian, relative entropy and quantum Fisher information of excited states in conformal field theory. 

In the second part, we consider holographic CFTs and show that quantum Fisher metric for ball shaped regions in vacuum is dual to the canonical energy of metric perturbations corresponding to the Rindler wedge of Anti-de Sitter space.

Aitor Lewkowycz, Princeton University

Towards a derivation of covariant holographic entanglement

Mark MezeiPrinceton University

Spread of entanglement and causality

We investigate causality constraints on the time evolution of entanglement entropy after a global quench. We analyze three models for the spread of entanglement: holographic quenches, the free particle streaming model of Calabrese and Cardy generalized to higher dimensions and an arbitrary pattern of entanglement, and a particle model with an infinite scattering rate. In these models we exhibit the intricate interplay of causality, strong subadditivity, and maximally entangled subsystems. Finally, using strong subadditivity we prove that the normalized rate of growth of entanglement entropy is bounded by the speed of light.

Jonathan Oppenheim, University College London

Do black holes create polyamory?

Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. In the latter case, one is violating the semi-classical causal structure of space, which is a strictly weaker implication than cloning or non-monogamy. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system. A particular example of this is the Horowitz-Maldacena proposal, and we argue that it needn't lead to cloning or violations of entanglement monogamy. In the case of the AMPS firewall experiment we find that the entanglement structure is modified, and one must have entanglement between the infalling Hawking partners and early time outgoing Hawking radiation which surprisingly tame violation of entanglement monogamy. http://arxiv.org/abs/1506.07133

Fernando Pastawski, California Institute of Technology

Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence

In this talk I will introduce a family of exactly solvable toy models of a holographic correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. The building block for these models are a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the holographic correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. I will describe how bulk operators may be represented on the boundary regions mimicking the Rindler-wedge reconstruction.

Xiao-Liang Qi, Stanford University

Holographic mapping, quantum error correction code and sub-AdS locality

In recent years, tensor networks have been proposed as a useful framework for understanding holographic duality, especially the relation between quantum entanglement and space-time geometry. Most tensor networks studied so far are defined in the large scale compared with AdS radius. In this talk, I will describe a new tensor network approach which defines a holographic mapping that applies to a refined network with sub-AdS scale resolution, or even to a flat space. The idea of quantum error correction code plays an essential role in this approach. Using this new tensor network, we can study features of the bulk theory, such as how locality at sub-AdS scale emerges in a "low energy subspace" even though the whole theory is intrinsically nonlocal, as a quantum gravity theory should be.

Mukund Rangamani, University of Durham

Positivity, negativity, entanglement, and holography

Subir Sachdev, Harvard University

Bekenstein-Hawking entropy and strange metals

Grant Salton, Standford University

Replicating Quantum Information in Spacetime

Tadashi TakayanagiYukawa Institute for Theoretical Physics, Kyoto University

Gravity Dual of Quantum Information Metric

We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

Aron Wall, Institute for Advanced Study

Entropic Focussing

Beni YoshidaCalifornia Institute of Technology

Order parameter for chaos 

The fact that a black hole is a fast-scrambler is at the heart of black hole information paradoxes. It has been suggested that chaos can be diagnosed by using an out-of-time correlation function, which is closely related to the commutator of operators separated in time. In this talk I propose that the tripartite information (also known as topological entanglement entropy) can be used as a quantitative information theoretic measure of chaos. By viewing a quantum channel as a state via the Choi-Jamilkowski isomorphism, the tripartite information measures four-party entanglement between the “past” and the “future”, much like an out-of-time correlation function. I will compute the time-evolution of the tripartite information for three systems; (a) non-integrable spin systems on a lattice, (b) planar networks of perfect tensors which mimic the growth of the Einstein-Rosen bridge and (c) a holographic system. This talk is based on an ongoing work with Xiaoliang Qi and Daniel Roberts. 

 

 

Tuesday Aug 18, 2015
Speaker(s): 

In this talk I will introduce a family of exactly solvable toy models of a holographic correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. The building block for these models are a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators.

 

Monday Aug 17, 2015
Speaker(s): 

Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected.

Scientific Organizers:

  • Rob Myers, Perimeter Institute
  • Mark van Raamsdonk, University of British Columbia
  • Guifre Vidal, Perimeter Institute