Entanglement rates and area laws
Quantum Physics
2013-11-06 v3 Strongly Correlated Electrons
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1304.5931,
title = {Entanglement rates and area laws},
author = {Karel Van Acoleyen and Michaël Mariën and Frank Verstraete},
journal= {arXiv preprint arXiv:1304.5931},
year = {2013}
}
Comments
v3: improved presentation of the SIE-proof, matching the published version