Entropy of a subalgebra of observables and the geometric entanglement entropy - INSPIRE

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Entropy of a subalgebra of observables and the geometric entanglement entropy

Jan 18, 2019

12 pages

Published in:

Phys.Rev.D 99 (2019) 8, 085001

Published: Apr 2, 2019

e-Print:

1901.06454 [hep-th]

DOI:

10.1103/PhysRevD.99.085001

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Abstract: (APS)

The geometric entanglement entropy of a quantum field in the vacuum state is known to be divergent and, when regularized, to scale as the area of the boundary of the region. Here, we introduce an operational definition of the entropy of the vacuum restricted to a region; we consider a subalgebra of observables that has support in the region and a finite resolution. We then define the entropy of a state restricted to this subalgebra. For Gaussian states, such as the vacuum of a free scalar field, we discuss how this entropy can be computed. In particular, we show that for a spherical region we recover an area law under a suitable refinement of the subalgebra.

Note:

21 pages, 4 figures

Formal aspects of field theory, field theory in curved space
entropy: entanglement
field theory: scalar
field theory
regularization
vacuum state
resolution

References(33)

Figures(5)

[1]

R.D. Sorkin

- Proceedings of the 10th International Conference on General Relativity and Gravitation Padova 1983

[2]

A Quantum Source of Entropy for Black Holes

- Phys.Rev.D 34 (1986) 373-383
•
DOI:
- 10.1103/PhysRevD.34.373

[3]

Entropy and area

Mark Srednicki
(
- UC, Berkeley, CfPA and
- LBL, Berkeley
)

- Phys.Rev.Lett. 71 (1993) 666-669
•
e-Print:
- hep-th/9303048
•
DOI:
- 10.1103/PhysRevLett.71.666

[4]

Entanglement entropy of black holes

Sergey N. Solodukhin
(
- Tours U., CNRS
)

- Living Rev.Rel. 14 (2011) 8
•
e-Print:
- 1104.3712
•
DOI:
- 10.12942/lrr-2011-8

[5]

Entanglement in many-body systems

Luigi Amico
(
- Catania U., DMFCI
)
,
Rosario Fazio
(
- NEST-INFM and
- SISSA, Trieste
)
,
Andreas Osterloh
(
- Hannover U.
)
,
Vlatko Vedral
(
- Leeds U.
)

- Rev.Mod.Phys. 80 (2008) 517-576
•
e-Print:
- quant-ph/0703044
•
DOI:
- 10.1103/RevModPhys.80.517

[6]

Quantum Information Meets Quantum Matter: From Quantum Entanglement to Topological Phases of Many-Body Systems

B. Zeng
,
X. Chen
,
D.L. Zhou
,
X.G. Wen

[7]

Mutual information and the F-theorem

- JHEP 10 (2015) 003
•
e-Print:
- 1506.06195
•
DOI:
- 10.1007/JHEP10(2015)003

[8]

Thermodynamics of space-time: The Einstein equation of state

Ted Jacobson
(
- Maryland U.
)

- Phys.Rev.Lett. 75 (1995) 1260-1263
•
e-Print:
- gr-qc/9504004
•
DOI:
- 10.1103/PhysRevLett.75.1260

[9]

Building up spacetime with quantum entanglement

Mark Van Raamsdonk
(
- British Columbia U.
)

- Gen.Rel.Grav. 42 (2010) 2323-2329,
- Int.J.Mod.Phys.D 19 (2010) 2429-2435
•
e-Print:
- 1005.3035
•
DOI:
- 10.1142/S0218271810018529

[9]

Building up spacetime with quantum entanglement

Mark Van Raamsdonk
(
- British Columbia U.
)

- Gen.Rel.Grav. 42 (2010) 2323-2329,
- Int.J.Mod.Phys.D 19 (2010) 2429-2435
•
e-Print:
- 1005.3035
•
DOI:
- 10.1142/S0218271810018529

[10]

On the Architecture of Spacetime Geometry

- Class.Quant.Grav. 31 (2014) 214002
•
e-Print:
- 1212.5183
•
DOI:
- 10.1088/0264-9381/31/21/214002

[11]

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

[12]

Entanglement Equilibrium and the Einstein Equation

Ted Jacobson
(
- Santa Barbara, KITP and
- Maryland U.
)

- Phys.Rev.Lett. 116 (2016) 20, 201101
•
e-Print:
- 1505.04753
•
DOI:
- 10.1103/PhysRevLett.116.201101

[13]

Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasifree States on Space-Times with a Bifurcate Killing Horizon

Bernard S. Kay
(
- Zurich U.
)
,
Robert M. Wald
(
- Chicago U., EFI and
- Chicago U.
)

- Phys.Rept. 207 (1991) 49-136
•
DOI:
- 10.1016/0370-1573(91)90015-E

[14]

Entanglement entropy in free quantum field theory

- J.Phys.A 42 (2009) 504007
•
e-Print:
- 0905.2562
•
DOI:
- 10.1088/1751-8113/42/50/504007

[15]

On the Quantum Structure of a Black Hole

Gerard 't Hooft
(
- Utrecht U.
)

- Nucl.Phys.B 256 (1985) 727-745
•
DOI:
- 10.1016/0550-3213(85)90418-3

[16]

Black hole entropy without brick walls

- Phys.Rev.D 52 (1995) 2245-2253
•
e-Print:
- gr-qc/9503003
•
DOI:
- 10.1103/PhysRevD.52.2245

[17]

Black hole entropy in canonical quantum gravity and superstring theory

- Phys.Rev.D 50 (1994) 2700-2711
•
e-Print:
- hep-th/9401070
•
DOI:
- 10.1103/PhysRevD.50.2700

[18]

On geometric entropy

- Phys.Lett.B 333 (1994) 55-61
•
e-Print:
- hep-th/9401072
•
DOI:
- 10.1016/0370-2693(94)91007-3

[19]

Remarks on the entanglement entropy for disconnected regions

- JHEP 03 (2009) 048
•
e-Print:
- 0812.1773
•
DOI:
- 10.1088/1126-6708/2009/03/048

[20]

Quantum Computation and Quantum Information

M. Nielsen
,
I. Chuang

[21]

Measuring entanglement entropy through the interference of quantum many-body twins

et al.

- Nature 528(7580):77-83 (2015)
•
e-Print:
- 1509.01160
•
DOI:
- 10.1038/nature15750

[22]

Local Quantum Physics: Fields, Particles, Algebras

R. Haag

[23]

Algebraic quantum field theory

Hans Halvorson
(
- Princeton U.
)
,
Michael Muger
(
- Nijmegen U.
)

[24]

Entanglement measures and their properties in quantum field theory

Stefan Hollands
(
- Leipzig U.
)
,
Ko Sanders
(
- Dublin City U.
)

e-Print:
- 1702.04924

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