Holographic coarse-grained states and the necessity of perfect entanglement - INSPIRE

DataBETA

Holographic coarse-grained states and the necessity of perfect entanglement

Yi-Yu Lin
(
- BIMSA, Beijing and
- Tsinghua U., Beijing
)
,
Jun Zhang
(
- Alabama U.
)

Dec 22, 2023

55 pages

Published in:

Phys.Rev.D 109 (2024) 12, 126012

Published: Jun 13, 2024

e-Print:

2312.14498 [hep-th]

DOI:

10.1103/PhysRevD.109.126012 (publication)

View in:

ADS Abstract Service

reference search4 citations

Citations per year

Abstract: (APS)

In the framework of the holographic principle, focusing on a central concept, conditional mutual information, we construct a class of coarse-grained states, which are intuitively connected to a family of thread configurations. These coarse-grained states characterize the entanglement structure of holographic systems at a coarse-grained level. Importantly, these coarse-grained states can be used to further reveal nontrivial requirements for the holographic entanglement structure. Specifically, we employ these coarse-grained states to probe the entanglement entropies of disconnected regions and the entanglement wedge cross section dual to the inherent correlation in a bipartite mixed state. The investigations demonstrate the necessity of perfect tensor state entanglement. Moreover, in a certain sense, our work establishes the equivalence between the holographic entanglement of purification and the holographic balanced partial entropy. We also construct a thread configuration with the multiscale entanglement renormalization ansatz (MERA) structure, reexamining the connection between the MERA structure and kinematic space.

Note:

55 pages, 22 figures

entanglement: structure
entropy: entanglement
holography
duality
family
kinematics
correlation
mixed state
renormalization

References(123)

Figures(42)

[1]

The Large N limit of superconformal field theories and supergravity

Juan Martin Maldacena
(
- Harvard U.
)

- Int.J.Theor.Phys. 38 (1999) 1113-1133 (reprint),
- Adv.Theor.Math.Phys. 2 (1998) 231-252
•
e-Print:
- hep-th/9711200
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a1

[2]

Gauge theory correlators from noncritical string theory

S.S. Gubser
(
- Princeton U.
)
,
Igor R. Klebanov
(
- Princeton U.
)
,
Alexander M. Polyakov
(
- Princeton U.
)

- Phys.Lett.B 428 (1998) 105-114
•
e-Print:
- hep-th/9802109
•
DOI:
- 10.1016/S0370-2693(98)00377-3

[3]

Anti-de Sitter space and holography

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Adv.Theor.Math.Phys. 2 (1998) 253-291
•
e-Print:
- hep-th/9802150
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a2

[4]

Holographic derivation of entanglement entropy from AdS/CFT

- Phys.Rev.Lett. 96 (2006) 181602
•
e-Print:
- hep-th/0603001
•
DOI:
- 10.1103/PhysRevLett.96.181602

[5]

Aspects of Holographic Entanglement Entropy

Shinsei Ryu
(
- Santa Barbara, KITP
)
,
Tadashi Takayanagi
(
- Kyoto U.
)

- JHEP 08 (2006) 045
•
e-Print:
- hep-th/0605073
•
DOI:
- 10.1088/1126-6708/2006/08/045

[6]

A Covariant holographic entanglement entropy proposal

Veronika E. Hubeny
(
- Durham U. and
- Durham U., Dept. of Math.
)
,
Mukund Rangamani
(
- Durham U. and
- Durham U., Dept. of Math.
)
,
Tadashi Takayanagi
(
- Kyoto U.
)

- JHEP 07 (2007) 062
•
e-Print:
- 0705.0016
•
DOI:
- 10.1088/1126-6708/2007/07/062

[7]

Entanglement Renormalization

G. Vidal
(
- Queensland U. and
- Caltech, IQI
)

- Phys.Rev.Lett. 99 (2007) 22, 220405
•
e-Print:
- cond-mat/0512165
•
DOI:
- 10.1103/PhysRevLett.99.220405

[8]

Class of Quantum Many-Body States That Can Be Efficiently Simulated

G. Vidal
(
- Queensland U.
)

- Phys.Rev.Lett. 101 (2008) 110501
•
e-Print:
- quant-ph/0610099
•
DOI:
- 10.1103/PhysRevLett.101.110501

[9]

Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz

- Phys.Rev.Lett. 115 (2015) 20, 200401
•
DOI:
- 10.1103/PhysRevLett.115.200401

[10]

Entanglement Renormalization and Holography

Brian Swingle
(
- MIT, LNS and
- Harvard U., Phys. Dept.
)

- Phys.Rev.D 86 (2012) 065007
•
e-Print:
- 0905.1317
•
DOI:
- 10.1103/PhysRevD.86.065007

[11]

Constructing holographic spacetimes using entanglement renormalization

Brian Swingle
(
- Harvard U., Phys. Dept.
)

e-Print:
- 1209.3304

[12]

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

Fernando Pastawski
(
- Caltech, IQI
)
,
Beni Yoshida
(
- Caltech, IQI
)
,
Daniel Harlow
(
- Princeton U. (main)
)
,
John Preskill
(
- Caltech, IQI
)

- JHEP 06 (2015) 149
•
e-Print:
- 1503.06237
•
DOI:
- 10.1007/JHEP06(2015)149

[13]

Holographic duality from random tensor networks

Patrick Hayden
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Sepehr Nezami
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Xiao-Liang Qi
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Nathaniel Thomas
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)
,
Michael Walter
(
- Stanford U., ITP and
- Stanford U., Phys. Dept.
)

et al.

- JHEP 11 (2016) 009
•
e-Print:
- 1601.01694
•
DOI:
- 10.1007/JHEP11(2016)009

[14]

Emergent Einstein Equation in p-adic Conformal Field Theory Tensor Networks

Lin Chen
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U.
)
,
Xirong Liu
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U.
)
,
Ling-Yan Hung
(
- Fudan U., Surf. Phys. Lab. and
- CICAM, Nanjing and
- Fudan U. and
- Fudan U., Shanghai and
- SQI, Shanghai
)

- Phys.Rev.Lett. 127 (2021) 22, 221602
•
e-Print:
- 2102.12022
•
DOI:
- 10.1103/PhysRevLett.127.221602

[15]

Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree

Lin Chen
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U. and
- Fudan U., Shanghai
)
,
Xirong Liu
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U. and
- Fudan U., Shanghai
)
,
Ling-Yan Hung
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U. and
- Fudan U., Shanghai
)

- JHEP 09 (2021) 097
•
e-Print:
- 2102.12024
•
DOI:
- 10.1007/JHEP09(2021)097

[16]

Bending the Bruhat-Tits tree. Part I. Tensor network and emergent Einstein equations

Lin Chen
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U. and
- Fudan U., Shanghai
)
,
Xirong Liu
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U. and
- Fudan U., Shanghai
)
,
Ling-Yan Hung
(
- Fudan U., Surf. Phys. Lab. and
- SQI, Shanghai and
- Fudan U. and
- Fudan U., Shanghai
)

- JHEP 06 (2021) 094
•
e-Print:
- 2102.12023
•
DOI:
- 10.1007/JHEP06(2021)094

[17]

Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT

Ning Bao
(
- UC, Berkeley
)
,
Geoffrey Penington
(
- Stanford U., ITP
)
,
Jonathan Sorce
(
- Stanford U., ITP
)
,
Aron C. Wall
(
- Cambridge U.
)

- JHEP 11 (2019) 069
•
e-Print:
- 1812.01171
•
DOI:
- 10.1007/JHEP11(2019)069

[18]

Holographic Tensor Networks in Full AdS/CFT

Ning Bao
(
- Stanford U., ITP
)
,
Geoffrey Penington
(
- Stanford U., ITP
)
,
Jonathan Sorce
(
- Stanford U., ITP
)
,
Aron C. Wall
(
- Stanford U., ITP
)

e-Print:
- 1902.10157

[19]

Entanglement Renormalization for Quantum Fields in Real Space

Jutho Haegeman
(
- Gent U.
)
,
Tobias J. Osborne
(
- Leibniz U., Hannover
)
,
Henri Verschelde
(
- Gent U.
)
,
Frank Verstraete
(
- Vienna U. and
- YITP, Stony Brook
)

- Phys.Rev.Lett. 110 (2013) 10, 100402
•
e-Print:
- 1102.5524
•
DOI:
- 10.1103/PhysRevLett.110.100402

[20]

Exact holographic mapping and emergent space-time geometry

Xiao-Liang Qi
(
- Stanford U., Phys. Dept.
)

e-Print:
- 1309.6282

[21]

Continuous Multiscale Entanglement Renormalization Ansatz as Holographic Surface-State Correspondence

- Phys.Rev.Lett. 115 (2015) 17, 171602
•
e-Print:
- 1506.01353
•
DOI:
- 10.1103/PhysRevLett.115.171602

[22]

Surface/State Correspondence as a Generalized Holography

- PTEP 2015 (2015) 7, 073B03
•
e-Print:
- 1503.03542
•
DOI:
- 10.1093/ptep/ptv089

[23]

${CFT}_{D}$ from ${TQFT}_{D + 1}$ via Holographic Tensor Network, and Precision Discretization of ${CFT}_{2}$

Lin Chen
(
- Fudan U., Surf. Phys. Lab. and
- Fudan U. and
- South China U. Tech.
)
,
Kaixin Ji
(
- Fudan U., Surf. Phys. Lab. and
- Fudan U.
)
,
Haochen Zhang
(
- Shandong U. and
- ICTP-AP, Beijing
)
,
Ce Shen
(
- Fudan U., Surf. Phys. Lab. and
- Fudan U.
)
,
Ruoshui Wang
(
- Cornell U.
)

et al.

- Phys.Rev.X 14 (2024) 4, 041033
•
e-Print:
- 2210.12127
•
DOI:
- 10.1103/PhysRevX.14.041033

[24]

Bulk Locality and Quantum Error Correction in AdS/CFT

Ahmed Almheiri
(
- Stanford U., Phys. Dept. and
- Stanford U., ITP
)
,
Xi Dong
(
- Stanford U., Phys. Dept. and
- Stanford U., ITP
)
,
Daniel Harlow
(
- Princeton U., CTP
)

- JHEP 04 (2015) 163
•
e-Print:
- 1411.7041
•
DOI:
- 10.1007/JHEP04(2015)163

[25]

Tensor network quotient takes the vacuum to the thermal state

Bartlomiej Czech
(
- Stanford U., Phys. Dept.
)
,
Glen Evenbly
(
- UC, Irvine
)
,
Lampros Lamprou
(
- Stanford U., Phys. Dept.
)
,
Samuel McCandlish
(
- Stanford U., Phys. Dept.
)
,
Xiao-Liang Qi
(
- Stanford U., Phys. Dept.
)

et al.

- Phys.Rev.B 94 (2016) 8, 085101
•
e-Print:
- 1510.07637
•
DOI:
- 10.1103/PhysRevB.94.085101

1-25 of 123
1
2
3
4
5
25 / page