Revision 2

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Title: Explicit Bell game separating commuting-operator and tensor-product quantum models
Plain: Quantum correlations can be modeled with a separate space for each lab or with commuting operators on one shared space. A 2020 result proved these give different correlations, but no explicit example is known.
Precise · changed · core: Revision 1: MIP* = RE (Ji, Natarajan, Vidick, Wright, Yuen, arXiv:2001.04383) implies a nonlocal game $G$ with finite inputs and outputs whose commuting-operator value $w_{qc}(G)$ exceeds its tensor-product value $w_{q}(G)$, resolving Tsirelson's problem negatively. Construct an explicit $G$, state its input size and gap, and certify $w_{qc}(G) > w_{q}(G)$.; Revision 2: $\mathrm{MIP}* = \mathrm{RE}$ (Ji, Natarajan, Vidick, Wright, Yuen, arXiv:2001.04383) implies a nonlocal game $G$ with finite inputs and outputs whose commuting-operator value $w_{qc}(G)$ exceeds its tensor-product value $w_{q}(G)$, resolving Tsirelson's problem negatively. Construct an explicit $G$, state its input size and gap, and certify $w_{qc}(G) > w_{q}(G)$.
Settled by: An explicit game with a certified upper bound on $w_q$ below a certified commuting-operator strategy value.
Kind: well-posed
Answer type: identification
References: (empty)
Literature status: partially-resolved
Status note: Existence follows from $\mathrm{MIP}* = \mathrm{RE}$ (2020); no explicit separating game was found in the literature checked.
Posed since: (empty)

Decisions