THE SET OF QUANTUM CORRELATIONS IS NOT CLOSED
By William Slofstra. Forum of Mathematics, Pi, 2017
209 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/06e8ee58ca61f731505d6f8fc64ca8b5b5daf0bc
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Tensor Products of C*-Algebras and Operator Spaces (2020, background): “See Slofstra’s [231, 232] (and Dykema and Paulsen’s [76]) for proofs that the set Qs(m, d) is not closed in general.”