Puzzles and pitfalls involving Haar-typicality in holography

doi:10.21468/SciPostPhys.4.6.033

Title: Puzzles and pitfalls involving Haar-typicality in holography

Abstract

Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.

Authors:

Bao, Ning ^[1];

^[2]

California Institute of Technology, University of California, Berkeley
California Institute of Technology

Publication Date:: 2018-06-19

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Gordon and Betty Moore Foundation

OSTI Identifier:: 1454886

Alternate Identifier(s):: OSTI ID: 1597657

Grant/Contract Number:: SC0011632; PHY-1125565; GBMF-12500028; 776

Resource Type:: Published Article

Journal Name:: SciPost Physics Proceedings

Additional Journal Information:: Journal Name: SciPost Physics Proceedings Journal Volume: 4 Journal Issue: 6; Journal ID: ISSN 2542-4653

Publisher:: SciPost Foundation

Country of Publication:: Netherlands

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS/CFT correspondence; Haar typicality; Holography

Citation Formats


                    Bao, Ning, and Chatwin-Davies, Aidan. Puzzles and pitfalls involving Haar-typicality in holography.  Netherlands: N. p., 2018. 
        Web.  doi:10.21468/SciPostPhys.4.6.033.

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                    Bao, Ning, & Chatwin-Davies, Aidan. Puzzles and pitfalls involving Haar-typicality in holography.  Netherlands.  doi:https://doi.org/10.21468/SciPostPhys.4.6.033

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                    Bao, Ning, and Chatwin-Davies, Aidan. Tue .  
        "Puzzles and pitfalls involving Haar-typicality in holography".  Netherlands.  doi:https://doi.org/10.21468/SciPostPhys.4.6.033.

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@article{osti_1454886,

  title        = {Puzzles and pitfalls involving Haar-typicality in holography},

  author       = {Bao, Ning and Chatwin-Davies, Aidan},

  abstractNote = {Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.},

  doi          = {10.21468/SciPostPhys.4.6.033},

  journal      = {SciPost Physics Proceedings},

  number       = 6,

  volume       = 4,

  place        = {Netherlands},

  year         = {2018},

  month        = {6}

}

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Title: Puzzles and pitfalls involving Haar-typicality in holography

Abstract

Citation Formats

Complexity as thermodynamic depth journal, November 1988

Information in black hole radiation journal, December 1993

Black holes as mirrors: quantum information in random subsystems journal, September 2007

Microcanonical phases of string theory on AdS m × S n journal, December 1998

The stretched horizon and black hole complementarity journal, October 1993

Typical event horizons in AdS/CFT journal, January 2016

An apologia for firewalls journal, September 2013

Black holes: complementarity or firewalls? journal, February 2013

The Black Hole Information Problem conference, January 2017

Average entropy of a subsystem journal, August 1993

Holographic duality from random tensor networks journal, November 2016

Moving the CFT into the bulk with T T ¯ $$ T\overline{T} $$ journal, April 2018

Black holes and the butterfly effect journal, March 2014

Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory journal, February 2005

Entanglement in Quantum Critical Phenomena journal, June 2003

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence journal, May 2006

Hyperinvariant Tensor Networks and Holography journal, October 2017

Bulk locality and quantum error correction in AdS/CFT journal, April 2015

Anti de Sitter space and holography journal, January 1998

Entropy of an n ‐system from its correlation with a k ‐reservoir journal, May 1978

A covariant holographic entanglement entropy proposal journal, July 2007

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence journal, June 2015

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality journal, July 2016

Entanglement entropy and quantum field theory journal, June 2004

Evolution of entanglement entropy in one-dimensional systems journal, April 2005

Time dependence of Hawking radiation entropy journal, September 2013

Particle creation by black holes journal, August 1975

Jerusalem lectures on black holes and quantum information journal, February 2016

Entanglement structures in qubit systems journal, August 2015

Holographic mutual information is monogamous journal, February 2013

Entanglement renormalization and holography journal, September 2012

The holographic entropy cone journal, September 2015

Complexity as thermodynamic depth
journal, November 1988

Information in black hole radiation
journal, December 1993

Black holes as mirrors: quantum information in random subsystems
journal, September 2007

Microcanonical phases of string theory on AdS _m × S ⁿ
journal, December 1998

The stretched horizon and black hole complementarity
journal, October 1993

Typical event horizons in AdS/CFT
journal, January 2016

An apologia for firewalls
journal, September 2013

Black holes: complementarity or firewalls?
journal, February 2013

The Black Hole Information Problem
conference, January 2017

Average entropy of a subsystem
journal, August 1993

Holographic duality from random tensor networks
journal, November 2016

Moving the CFT into the bulk with T T ¯ $$ T\overline{T} $$
journal, April 2018

Black holes and the butterfly effect
journal, March 2014

Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory
journal, February 2005

Entanglement in Quantum Critical Phenomena
journal, June 2003

Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
journal, May 2006

Hyperinvariant Tensor Networks and Holography
journal, October 2017

Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

Anti de Sitter space and holography
journal, January 1998

Entropy of an n ‐system from its correlation with a k ‐reservoir
journal, May 1978

A covariant holographic entanglement entropy proposal
journal, July 2007

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
journal, July 2016

Entanglement entropy and quantum field theory
journal, June 2004

Evolution of entanglement entropy in one-dimensional systems
journal, April 2005

Time dependence of Hawking radiation entropy
journal, September 2013

Particle creation by black holes
journal, August 1975

Jerusalem lectures on black holes and quantum information
journal, February 2016

Entanglement structures in qubit systems
journal, August 2015

Holographic mutual information is monogamous
journal, February 2013

Entanglement renormalization and holography
journal, September 2012

The holographic entropy cone
journal, September 2015