2015/06/23 by Laura Mančinska · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #cs.CC #math-ph #math.MP #quant-ph
published as Computing with New Resources, vol. 8808 of LNCS, pages 200--207, 2014 · In addition to the published material this version contains results on self testing
arxiv created 2015/06/23 · arxiv updated 2015/06/24
A pseudo-telepathy game is a nonlocal game which can be won with probability one using some finite-dimensional quantum strategy but not using a classical one. Our central question is whether there exist two-party pseudo-telepathy games which cannot be won with probability one using a maximally entangled state. Towards answering this question, we develop conditions under which maximally entangled states suffice. In particular, we show that maximally entangled states suffice for weak projection games which we introduce as a relaxation of projection games. Our results also imply that any pseudo-telepathy weak projection game yields a device-independent certification of a maximally entangled state. In particular, by establishing connections to the setting of communication complexity, we exhibit a class of games Gn for testing maximally entangled states of local dimension Ω(n). We leave the robustness of these self-tests as an open question.