Area law for random graph states
arXiv:1302.0709 · doi:10.1088/1751-8113/46/30/305302
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.
v2: minor typos corrected
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- On spectral distribution of sample covariance matrices from large dimensional and large -fold tensor products
- On the joint distribution of the marginals of multipartite random quantum states
- Entanglement entropy on finitely ramified graphs
- Random unitary matrices associated to a graph