Jordi Tura Brugués: Energy as a detector of nonlocality of many-body spin systems

Опубликовано 3 февраля 2017, 19:26

"We present a method to show that the ground states of some quantum many-body spin Hamiltonians in one spatial dimension are nonlocal.
We assign a Bell inequality to the given Hamiltonian in a natural way and we find its classical bound using dynamic programming. The Bell inequality is such that its quantum value corresponds to the ground state energy of the Hamiltonian, which we find it exactly by mapping the spin system to a quadratic system of fermions using the Jordan-Wigner transformation.
The method can also be used from the opposite point of view; namely, as a new method to optimize certain Bell inequalities.
In the translationally invariant (TI) case, we provide an exponentially faster solution of the classical bound and analytically closed expressions of the quantum value. We apply our method to three examples: a tight TI inequality for $8$ parties, a quasi TI uniparametric inequality for any even number of parties, and we show that the ground state of a spin glass is nonlocal in some parameter region. This opens the possibility for the use of ground states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality."