The Holographic Entropy Arrangement

Hubeny, Veronika E.; Rangamani, Mukund; Rota, Massimiliano

doi:10.1002/prop.201900011

Title: The Holographic Entropy Arrangement

Abstract

Here, we develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in [1], of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign-definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5-party entropy cone. Lastly, we work with explicit configurations in arbitrary (time-dependent) states leading to both simple derivationsmore »« less

Authors:

Hubeny, Veronika E. ^[1]; Rangamani, Mukund ^[2]; Rota, Massimiliano ^[3]

Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
Univ. of California, Davis, CA (United States). Center for Quantum Mathematics and Physics (QMAP)
Univ. of California, Santa Barbara, CA (United States)

Publication Date:: Wed Feb 27 00:00:00 EST 2019

Research Org.:: Univ. of California, Davis, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Science Foundation (NSF)

OSTI Identifier:: 1596290

Alternate Identifier(s):: OSTI ID: 1497238

Grant/Contract Number:: SC0009999; SC0019480; PHY17‐48958

Resource Type:: Accepted Manuscript

Journal Name:: Fortschritte der Physik

Additional Journal Information:: Journal Volume: 67; Journal Issue: 4; Journal ID: ISSN 0015-8208

Publisher:: Wiley

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; holography; multipartite entanglement

Citation Formats


                    Hubeny, Veronika E., Rangamani, Mukund, and Rota, Massimiliano. The Holographic Entropy Arrangement.  United States: N. p., 2019. 
Web.  doi:10.1002/prop.201900011.

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                    Hubeny, Veronika E., Rangamani, Mukund, & Rota, Massimiliano. The Holographic Entropy Arrangement.  United States.  https://doi.org/10.1002/prop.201900011

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                    Hubeny, Veronika E., Rangamani, Mukund, and Rota, Massimiliano. Wed .  
"The Holographic Entropy Arrangement".  United States.  https://doi.org/10.1002/prop.201900011.  https://www.osti.gov/servlets/purl/1596290.

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@article{osti_1596290,

  title        = {The Holographic Entropy Arrangement},

  author       = {Hubeny, Veronika E. and Rangamani, Mukund and Rota, Massimiliano},

  abstractNote = {Here, we develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in [1], of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign-definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5-party entropy cone. Lastly, we work with explicit configurations in arbitrary (time-dependent) states leading to both simple derivations and an intuitive picture of the entanglement pattern.},

  doi          = {10.1002/prop.201900011},

  journal      = {Fortschritte der Physik},

  number       = 4,

  volume       = 67,

  place        = {United States},

  year         = {Wed Feb 27 00:00:00 EST 2019},

  month        = {Wed Feb 27 00:00:00 EST 2019}

}

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Quantum corrections to holographic entanglement entropy
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Chaos in quantum channels
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Hubeny, Veronika E.
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Hubeny, Veronika E.; Rangamani, Mukund; Rota, Massimiliano
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Structure of states which satisfy strong subadditivity of quantum entropy with equality
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Works referencing / citing this record:

The Holographic Entropy Cone for Five Regions
text, January 2019

Hernández-Cuenca, Sergio
arXiv
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Holographic Entropy Relations Repackaged
text, January 2019

He, Temple; Headrick, Matthew; Hubeny, Veronika E.
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Avis, David; Hernández-Cuenca, Sergio
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The Holographic Entropy Cone for Five Regions
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Holographic Entropy Relations Repackaged
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He, Temple; Headrick, Matthew; Hubeny, Veronika E.
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Wormhole Traversability via Quantum Random Walks
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Bao, Ning; Su, Vincent P.; Usatyuk, Mykhaylo
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Optimized Correlation Measures in Holography
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Large-$d$ phase transitions in holographic mutual information
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Colin-Ellerin, Sean; Hubeny, Veronika E.; Niehoff, Benjamin E.
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The quantum marginal independence problem
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Hernández-Cuenca, Sergio; Hubeny, Veronika E.; Rangamani, Mukund
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A Gap Between the Hypergraph and Stabilizer Entropy Cones
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SU(N)1 Chern-Simons theory, the Clifford group, and Entropy Cone
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Title: The Holographic Entropy Arrangement

Abstract

Citation Formats

Building up spacetime with quantum entanglement journal, June 2010

The gravity dual of Rényi entropy journal, August 2016

Quantum quenches in 1 + 1 dimensional conformal field theories journal, June 2016

Chaos in quantum channels journal, February 2016

Bulk locality and cooperative flows journal, December 2018

Lectures on Gravity and Entanglement conference, January 2017

Cool horizons for entangled black holes journal, August 2013

Quantum Entanglement Growth under Random Unitary Dynamics journal, July 2017

Bit Threads and Holographic Entanglement journal, November 2016

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

APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory journal, October 2018

Detecting Topological Order in a Ground State Wave Function journal, March 2006

Topological Entanglement Entropy journal, March 2006

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy journal, November 2014

Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality journal, April 2004

All the entropies on the light-cone journal, May 2018

A covariant holographic entanglement entropy proposal journal, July 2007

The structure of Rényi entropic inequalities journal, October 2013

Multivariate information transmission journal, September 1954

Quantum corrections to holographic entanglement entropy journal, November 2013

Holographic Entropy Relations journal, September 2018

Entanglement detection journal, April 2009

The inequalities of quantum information theory journal, April 2003

Quantum entanglement journal, June 2009

The holographic entropy cone journal, September 2015

Multivariate information transmission journal, June 1954

A Covariant Holographic Entanglement Entropy Proposal text, January 2007

Cool horizons for entangled black holes text, January 2013

Quantum corrections to holographic entanglement entropy text, January 2013

Chaos in quantum channels text, January 2015

Bulk locality and cooperative flows text, January 2018

Holographic entropy relations text, January 2018

Structure of states which satisfy strong subadditivity of quantum entropy with equality text, January 2003

Quantum entanglement text, January 2007

Quantum corrections to holographic entanglement entropy text, January 2013

The Holographic Entropy Cone for Five Regions text, January 2019

Holographic Entropy Relations Repackaged text, January 2019

On the foundations and extremal structure of the holographic entropy cone journal, March 2023

The Holographic Entropy Cone for Five Regions text, January 2019

Holographic Shannon Entropy: The Outer Entropy of Entanglement Wedges preprint, January 2019

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Wormhole Traversability via Quantum Random Walks preprint, January 2019

Optimized Correlation Measures in Holography text, January 2019

Large-$d$ phase transitions in holographic mutual information text, January 2019

The quantum marginal independence problem preprint, January 2019

A Gap Between the Hypergraph and Stabilizer Entropy Cones preprint, January 2020

SU(N)1 Chern-Simons theory, the Clifford group, and Entropy Cone preprint, January 2020

Building up spacetime with quantum entanglement
journal, June 2010

The gravity dual of Rényi entropy
journal, August 2016

Quantum quenches in 1 + 1 dimensional conformal field theories
journal, June 2016

Chaos in quantum channels
journal, February 2016

Bulk locality and cooperative flows
journal, December 2018

Lectures on Gravity and Entanglement
conference, January 2017

Cool horizons for entangled black holes
journal, August 2013

Quantum Entanglement Growth under Random Unitary Dynamics
journal, July 2017

Bit Threads and Holographic Entanglement
journal, November 2016

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

APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory
journal, October 2018

Detecting Topological Order in a Ground State Wave Function
journal, March 2006

Topological Entanglement Entropy
journal, March 2006

Maximin surfaces, and the strong subadditivity of the covariant holographic entanglement entropy
journal, November 2014

Structure of States Which Satisfy Strong Subadditivity of Quantum Entropy with Equality
journal, April 2004

All the entropies on the light-cone
journal, May 2018

A covariant holographic entanglement entropy proposal
journal, July 2007

The structure of Rényi entropic inequalities
journal, October 2013

Multivariate information transmission
journal, September 1954

Quantum corrections to holographic entanglement entropy
journal, November 2013

Holographic Entropy Relations
journal, September 2018

Entanglement detection
journal, April 2009

The inequalities of quantum information theory
journal, April 2003

Quantum entanglement
journal, June 2009

The holographic entropy cone
journal, September 2015

Multivariate information transmission
journal, June 1954

A Covariant Holographic Entanglement Entropy Proposal
text, January 2007

Cool horizons for entangled black holes
text, January 2013

Quantum corrections to holographic entanglement entropy
text, January 2013

Chaos in quantum channels
text, January 2015

Bulk locality and cooperative flows
text, January 2018

Holographic entropy relations
text, January 2018

Structure of states which satisfy strong subadditivity of quantum entropy with equality
text, January 2003

Quantum entanglement
text, January 2007

Quantum corrections to holographic entanglement entropy
text, January 2013

The Holographic Entropy Cone for Five Regions
text, January 2019

Holographic Entropy Relations Repackaged
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On the foundations and extremal structure of the holographic entropy cone
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Holographic Shannon Entropy: The Outer Entropy of Entanglement Wedges
preprint, January 2019

Holographic Entropy Relations Repackaged
text, January 2019

Wormhole Traversability via Quantum Random Walks
preprint, January 2019

Optimized Correlation Measures in Holography
text, January 2019

Large-$d$ phase transitions in holographic mutual information
text, January 2019

The quantum marginal independence problem
preprint, January 2019

A Gap Between the Hypergraph and Stabilizer Entropy Cones
preprint, January 2020

SU(N)1 Chern-Simons theory, the Clifford group, and Entropy Cone
preprint, January 2020