Advertisement

Journal of High Energy Physics

, 2019:118 | Cite as

Holographic entropy relations repackaged

  • Temple HeEmail author
  • Matthew Headrick
  • Veronika E. Hubeny
Open Access
Regular Article - Theoretical Physics
First Online:
  • 26 Downloads

Abstract

We explore the structure of holographic entropy relations (associated with ‘information quantities’ given by a linear combination of entanglement entropies of spatial sub-partitions of a CFT state with geometric bulk dual). Such entropy relations can be recast in multiple ways, some of which have significant advantages. Motivated by the already-noted simplification of entropy relations when recast in terms of multipartite information, we explore additional simplifications when recast in a new basis, which we dub the K-basis, constructed from perfect tensor structures. For the fundamental information quantities such a recasting is surprisingly compact, in part due to the interesting fact that entropy vectors associated to perfect tensors are in fact extreme rays in the holographic entropy cone (as well as the full quantum entropy cone). More importantly, we prove that all holographic entropy inequalities have positive coefficients when expressed in the K-basis, underlying the key advantage over the entropy basis or the multipartite information basis.

Keywords

AdS-CFT Correspondence Conformal Field Theory 
Download to read the full article text

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

References

  1. [1]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    V.E. Hubeny, M. Rangamani and T. Takayanagi, A Covariant holographic entanglement entropy proposal, JHEP07 (2007) 062 [arXiv:0705.0016] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    M. Van Raamsdonk, Building up spacetime with quantum entanglement, Gen. Rel. Grav.42 (2010) 2323 [arXiv:1005.3035] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    J. Maldacena and L. Susskind, Cool horizons for entangled black holes, Fortsch. Phys.61 (2013) 781 [arXiv:1306.0533] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    M. Rangamani and T. Takayanagi, Holographic Entanglement Entropy, Lect. Notes Phys.931 (2017) 1 [arXiv:1609.01287] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  6. [6]
    E. Witten, APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory, Rev. Mod. Phys.90 (2018) 045003 [arXiv:1803.04993] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    M. Headrick and T. Takayanagi, A Holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev.D 76 (2007) 106013 [arXiv:0704.3719] [INSPIRE].
  8. [8]
    P. Hayden, M. Headrick and A. Maloney, Holographic Mutual Information is Monogamous, Phys. Rev.D 87 (2013) 046003 [arXiv:1107.2940] [INSPIRE].
  9. [9]
    A.C. Wall, Maximin Surfaces and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy, Class. Quant. Grav.31 (2014) 225007 [arXiv:1211.3494] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    E.H. Lieb and M.B. Ruskai, Proof of the strong subadditivity of quantum-mechanical entropy, J. Math. Phys.14 (1973) 1938 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    V.E. Hubeny, Bulk locality and cooperative flows, JHEP12 (2018) 068 [arXiv:1808.05313] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    S.X. Cui, P. Hayden, T. He, M. Headrick, B. Stoica and M. Walter, Bit Threads and Holographic Monogamy, arXiv:1808.05234 [INSPIRE].
  13. [13]
    M. Freedman and M. Headrick, Bit threads and holographic entanglement, Commun. Math. Phys.352 (2017) 407 [arXiv:1604.00354] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    N. Bao, S. Nezami, H. Ooguri, B. Stoica, J. Sully and M. Walter, The Holographic Entropy Cone, JHEP09 (2015) 130 [arXiv:1505.07839] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  15. [15]
    V.E. Hubeny, M. Rangamani and M. Rota, Holographic entropy relations, Fortsch. Phys.66 (2018) 1800067 [arXiv:1808.07871] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  16. [16]
    V.E. Hubeny, M. Rangamani and M. Rota, The holographic entropy arrangement, Fortsch. Phys.67 (2019) 1900011 [arXiv:1812.08133] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  17. [17]
    S. Hernández Cuenca, Holographic entropy cone for five regions, Phys. Rev.D 100 (2019) 026004 [arXiv:1903.09148] [INSPIRE].
  18. [18]
    D. Marolf, M. Rota and J. Wien, Handlebody phases and the polyhedrality of the holographic entropy cone, JHEP10 (2017) 069 [arXiv:1705.10736] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    H. Maxfield, S. Ross and B. Way, Holographic partition functions and phases for higher genus Riemann surfaces, Class. Quant. Grav.33 (2016) 125018 [arXiv:1601.00980] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  20. [20]
    S. Hernández Cuenca, V.E. Hubeny, M. Rangamani and M. Rota, to appear.Google Scholar
  21. [21]
    P. Hayden, S. Nezami, X.-L. Qi, N. Thomas, M. Walter and Z. Yang, Holographic duality from random tensor networks, JHEP11 (2016) 009 [arXiv:1601.01694] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  22. [22]
    W. Helwig, W. Cui, A. Riera, J.I. Latorre and H.-K. Lo, Absolute Maximal Entanglement and Quantum Secret Sharing, Phys. Rev.A 86 (2012) 052335 [arXiv:1204.2289] [INSPIRE].
  23. [23]
    D.N. Page, Information in black hole radiation, Phys. Rev. Lett.71 (1993) 3743 [hep-th/9306083] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Quantum Mathematics and Physics (QMAP), Department of PhysicsUniversity of CaliforniaDavisU.S.A.
  2. 2.Martin Fisher School of PhysicsBrandeis UniversityWalthamU.S.A.

Personalised recommendations