Deriving Three-Outcome Permutationally Invariant Bell Inequalities

Entropy, vol. 26, pp. 816

Abstract

We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with N observers, each of which performs one out of two possible three-outcome measurements on their share of the system. As the complexity of the set of classical correlations prohibits its full characterization in this multipartite scenario, we consider its projection to a lower-dimensional subspace spanned by permutationally invariant one- and two-body observables. This simplification allows us to formulate two complementary methods for detecting nonlocality in multipartite three-level systems, both having a complexity independent of N. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles.

Authors 4

1. Albert Aloy

   University of Vienna · Austrian Academy of Sciences · Vienna Center for Quantum Science and Technology

   Affiliation as printed

   Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria

   Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, 1090 Vienna, Austria

2. Guillem Müller-Rigat

   Institute of Photonic Sciences · Barcelona Institute of Science and Technology

   Affiliation as printed

   ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain

3. Jordi Tura Aachen Instituut-Lorentz 〈<i>aQa^L</i>〉 Applied Quantum Algorithms Leiden 〈aQaL〉 Applied Quantum Algorithms – Leiden

   Leiden University

   Affiliation as printed

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands

   〈<i>aQa^L</i>〉 Applied Quantum Algorithms Leiden, 2300 RA Leiden, The Netherlands

   〈aQaL〉 Applied Quantum Algorithms Leiden, 2300 RA Leiden, The Netherlands

4. Matteo Fadel corresponding

   ETH Zurich

   Affiliation as printed

   Department of Physics, ETH Zürich, 8093 Zürich, Switzerland