Near-Optimal and Explicit Bell Inequality Violations

Understand

Entangled quantum systems can exhibit correlations that cannot be simulated classically.

• For historical reasons such correlations are called "Bell inequality violations." We give two new two-player games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work.
• The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by Bar-Yossef, Jayram, and Kerenidis.
• This game can be won with probability 1 by a strategy using a maximally entangled state with local dimension $n$ (e.g., $\log n$ EPR-pairs), while we show that the winning probability of any classical strategy differs from ${1}/{2}$ by at most $O((\log n)/\sqrt{n})$.