Abstract
We present a method to show that low-energy states of quantum many-body 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 quasi-TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a nonintegrable interacting -like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.
2 More- Received 4 September 2016
DOI:https://doi.org/10.1103/PhysRevX.7.021005
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Classical correlations are part of our everyday experience. If one always puts on a pair of socks of the same color and shape, for example, looking at the color and shape of one sock determines the color and shape of the other. In nature, there exists a very weird form of correlations that are called nonlocal, which are shown by some entangled states among atomic particles. By making the minimal assumptions that properties of objects (shape/color) exist regardless of our knowledge of them, and that information cannot propagate instantaneously, one finds that quantum physics can produce correlations incompatible with these two apparently reasonable principles. These nonlocal correlations are the object of study in our paper. We are interested in learning whether these correlations appear in a natural way: more precisely, as ground states of spin Hamiltonians (a mathematical description of the energy) that appear in some physical systems.
The characterization of nonlocal correlations in quantum systems composed of many particles is a very complicated problem. We propose a simple test for nonlocal correlations in many-body systems: for example, electrons (described by their spin degree of freedom) in a system of one spatial dimension. By combining numerical and analytical results, we show that some Hamiltonians that have been studied by physicists for several decades have a state of minimal energy that can display nonlocal correlations. This sheds some light onto this fascinating problem, which we hope sparks further progress in our understanding of nonlocality in quantum many-body systems.