Entanglement rates and area laws

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.

v3: improved presentation of the SIE-proof, matching the published version

References in corpus (3)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Upper bounds on entangling rates of bipartite Hamiltonians
• Almost All Quantum States Have Low Entropy Rates for Any Coupling to the Environment

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