The set of quantum correlations is not closed

2017/03/24 by Slofstra, William · 8 citations
#FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.1703.08618

Abstract

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.

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