### 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 language | English (US) |
---|---|

Article number | 086013 |

Journal | Physical Review D |

Volume | 99 |

Issue number | 8 |

DOIs | |

State | Published - Apr 15 2019 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*99*(8), [086013]. https://doi.org/10.1103/PhysRevD.99.086013

}

*Physical Review D*, vol. 99, no. 8, 086013. https://doi.org/10.1103/PhysRevD.99.086013

**Entanglement entropy of Bell-network states in loop quantum gravity : Analytical and numerical results.** / Bianchi, Eugenio; Donà, Pietro; Vilensky, Ilya.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Entanglement entropy of Bell-network states in loop quantum gravity

T2 - Analytical and numerical results

AU - Bianchi, Eugenio

AU - Donà, Pietro

AU - Vilensky, Ilya

PY - 2019/4/15

Y1 - 2019/4/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85065104161&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065104161&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.99.086013

DO - 10.1103/PhysRevD.99.086013

M3 - Article

AN - SCOPUS:85065104161

VL - 99

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 8

M1 - 086013

ER -