  We construct a linear system non-local game which can be played perfectly
using a limit of finite-dimensional quantum strategies, but which cannot be
played perfectly on any finite-dimensional Hilbert space, or even with any
tensor-product strategy. In particular, this shows that the set of
(tensor-product) quantum correlations is not closed. The constructed non-local
game provides another counterexample to the "middle" Tsirelson problem, with a
shorter proof than our previous paper (though at the loss of the universal
embedding theorem). We also show that it is undecidable to determine if a
linear system game can be played perfectly with a finite-dimensional strategy,
or a limit of finite-dimensional quantum strategies.
