Area law for random graph states

TL;DR

This paper studies the entanglement properties of random graph states, demonstrating that they generally obey an area law with corrections depending on the graph topology, which has implications for quantum network entanglement distribution.

Contribution

It establishes that random graph states satisfy an area law for entanglement entropy, including corrections for complex topologies, extending understanding of entanglement in quantum networks.

Findings

Area law holds exactly for non-crossing partitions.

Average entanglement entropy obeys an area law with topology-dependent corrections.

Results applicable to quantum network entanglement distribution.

Abstract

Random pure states of multi-partite quantum systems, associated with arbitrary graphs, are investigated. Each vertex of the graph represents a generic interaction between subsystems, described by a random unitary matrix distributed according to the Haar measure, while each edge of the graph represents a bi-partite, maximally entangled state. For any splitting of the graph into two parts we consider the corresponding partition of the quantum system and compute the average entropy of entanglement. First, in the special case where the partition does not "cross" any vertex of the graph, we show that the area law is satisfied exactly. In the general case, we show that the entropy of entanglement obeys an area law on average, this time with a correction term that depends on the topologies of the graph and of the partition. The results obtained are applied to the problem of distribution of quantum entanglement in a quantum network with prescribed topology.