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.
1 More- Received 28 December 2018
DOI:https://doi.org/10.1103/PhysRevD.99.086013
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