Abstract
We construct a linear system nonlocal 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 nonlocal 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.
Publisher
Cambridge University Press (CUP)
Subject
Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Analysis
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