Entanglement Rates and Area Laws
Category: Scientific HighlightsPublished in Physical Review Letters
ABSTRACT:
We prove an upper bound on the maximal rate at which a Hamiltonian interaction can generate entanglement in a bipartite system. The scaling of this bound as a function of the subsystem dimension on which the Hamiltonian acts nontrivially is optimal and is exponentially improved over previously known bounds. As an application, we show that a gapped quantum many-body spin system on an arbitrary lattice satisfies an area law for the entanglement entropy if and only if any other state with which it is adiabatically connected (i.e., any state in the same phase) also satisfies an area law.
Figure: The balls of support (for the Manhattan metric) centered at two points i and j, for two terms ki(s,4) and kj(s,2) in the Hamiltonian K(s). Only the term ki(s,4) can generate entanglement across the cut. |
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Van Acoleyen K., Mariën M., Verstraete F. (2013), Entanglement Rates and Area Laws, Phys. Rev. Lett. 111, 170501. DOI:10.1103/PhysRevLett.111.170501
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