Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results - INSPIRE

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Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results

Eugenio Bianchi
(
- Penn State U., University Park, IGC and
- Penn State U.
)
,
Pietro Donà
(
- Penn State U., University Park, IGC and
- Penn State U.
)
,
Ilya Vilensky
(
- Florida Atlantic U.
)

Dec 28, 2018

13 pages

Published in:

Phys.Rev.D 99 (2019) 8, 086013

Published: Apr 17, 2019

e-Print:

1812.10996 [gr-qc]

DOI:

10.1103/PhysRevD.99.086013 (publication)

Report number:

IGC-18/12-1

View in:

reference search21 citations

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Abstract: (APS)

Bell-network states are loop-quantum-gravity states that glue quantum polyhedra with entanglement. We present an algorithm and a code that evaluates the reduced density matrix of a Bell-network state and computes its entanglement entropy. In particular, we use our code for simple graphs to study properties of Bell-network states and to show that they are nontypical in the Hilbert space. Moreover, we investigate analytically Bell-network states on arbitrary finite graphs. We develop methods to compute the Rényi entropy of order p for a restriction of the state to an arbitrary region. In the uniform large-spin regime, we determine bounds on the entanglement entropy and show that it obeys an area law. Finally, we discuss the implications of our results for correlations of geometric observables.

Note:

26 pages, 5 figures. The code is available at the link https://bitbucket.org/pietrodona/bellnetworkentropy. Updated to match the published version

String theory, quantum gravity, gauge/gravity duality
entropy: entanglement
quantum gravity: loop space
density matrix: reduced
numerical calculations
network

References(67)

Figures(13)

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