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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.
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Laura Manc̆inska and Thomas Vidick, Unbounded Entanglement Can Be Needed to Achieve the Optimal Success Probability , Automata, Languages, and Programming, Lecture Notes in Computer Science, no. 8572, Springer Berlin Heidelberg, 2014, pp. 835–846
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Debbie Leung and Bingjie Wang, in preparation
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Sabine Burgdorf, Monique Laurent, and Teresa Piovesan, On the closure of the completely positive semidefinite cone and linear approximations to quantum colorings , Electronic Journal of Linear Algebra 32
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