Tsirelson's problem and an embedding theorem for groups arising from non-local games

Understand

Tsirelson's problem asks whether the commuting operator model for two-party quantum correlations is equivalent to the tensor-product model.

• We give a negative answer to this question by showing that there are non-local games which have perfect commuting-operator strategies, but do not have perfect tensor-product strategies.
• The weak Tsirelson problem, which is known to be equivalent to Connes embedding problem, remains open.
• The examples we construct are instances of (binary) linear system games.