THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED

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-p...

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Bibliographic Details
Published inForum of mathematics. Pi Vol. 7
Main Author SLOFSTRA, WILLIAM
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 2019
Subjects
20F05 (secondary)
81P45 (primary)
Game theory
Games
Hilbert space
Mathematical analysis
Tensors
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ISSN2050-5086
2050-5086
DOI10.1017/fmp.2018.3

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Summary: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.
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ISSN:2050-5086
2050-5086
DOI:10.1017/fmp.2018.3