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arXiv · 1812.10996

Entanglement entropy of Bell-network states in LQG: Analytical and numerical results

Eugenio Bianchi·Pietro Dona·Ilya Vilensky
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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 non-typical in the Hilbert space. Moreover, we investigate analytically Bell-network states on arbitrary finite graphs. We develop methods to compute the R\'enyi 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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Eugenio Bianchi, Pietro Dona, Ilya Vilensky. 2018-12-28. Entanglement entropy of Bell-network states in LQG: Analytical and numerical results. https://doi.org/10.1103/physrevd.99.086013

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