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

Eugenio Bianchi, Pietro Donà, Ilya Vilensky

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Article number086013
JournalPhysical Review D
Volume99
Issue number8
DOIs
StatePublished - Apr 15 2019

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bells
entropy
gravitation
glues
Hilbert space
polyhedrons
constrictions

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

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title = "Entanglement entropy of Bell-network states in loop quantum gravity: Analytical and numerical results",
abstract = "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 R{\'e}nyi 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.",
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Entanglement entropy of Bell-network states in loop quantum gravity : Analytical and numerical results. / Bianchi, Eugenio; Donà, Pietro; Vilensky, Ilya.

In: Physical Review D, Vol. 99, No. 8, 086013, 15.04.2019.

Research output: Contribution to journalArticle

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AU - Donà, Pietro

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