Bell violations through independent bases games (pp0009-0020)
          Oded Regev
          doi: https://doi.org/10.26421/QIC12.1-2-2
Abstracts: In a recent paper, Junge and Palazuelos presented two two-player games exhibiting interesting properties. In their first game, entangled players can perform notably better than classical players. The quantitative gap between the two cases is remarkably large, especially as a function of the number of inputs to the players. In their second game, entangled players can perform notably better than players that are restricted to using a maximally entangled state (of arbitrary dimension). This was the first game exhibiting such a behavior. The analysis of both games is heavily based on non-trivial results from Banach space theory and operator space theory. Here we provide alternative proofs of these two results. Our proofs are arguably simpler, use elementary probabilistic techniques and standard quantum information arguments, and also give better quantitative bounds.
Key words: Bell inequality violations, maximally entangled state, random access codes