Energy as a Detector of Nonlocality of ManyBody Spin Systems
Abstract
We present a method to show that lowenergy states of quantum manybody interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programing. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI) case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for eight parties, a quasiTI uniparametric inequality for any even number of parties, ground states of spinglass systems, and a nonintegrable interacting X X Z like Hamiltonian. Our work opens the possibility for the use of lowenergy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.
 Publication:

Physical Review X
 Pub Date:
 April 2017
 DOI:
 10.1103/PhysRevX.7.021005
 arXiv:
 arXiv:1607.06090
 Bibcode:
 2017PhRvX...7b1005T
 Keywords:

 Quantum Physics
 EPrint:
 21 pages (14 + appendices), 9 figures, 2 tables. A new example is added and minor changes have been made. This version is closer to the published one