Simplest bipartite perfect quantum strategies

Abstract

A bipartite perfect quantum strategy (BPQS) allows two players who cannot communicate with each other to always win a nonlocal game. BPQSs are rare but fundamental in light of some recent results in quantum information, computation, and foundations. A more than 40-year-old open problem is how many inputs (measurement settings) a BPQS requires. A related problem is how many inputs are needed if, in addition, the quantum system has minimum dimension. A third, apparently unrelated, problem is what is the connection between BPQSs and state-independent contextuality, which inspired the first BPQSs. Here, we solve the third problem: we prove that {\em every} BPQS defines a Kochen-Specker set. We use this result to identify the BPQS with the smallest number of inputs, both in the general case and in the case of minimum dimension, and solve some related problems. We conjecture that the BPQSs presented here are the solutions to the first two problems.

6 pages, 2 figures

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Cited by in corpus (7)

• The simplest Kochen-Specker set
• Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
• Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
• All genuinely entangled stabilizer subspaces are multipartite fully nonlocal
• How contextuality and antidistinguishability are related
• Supersinglets can be self-tested with perfect quantum strategies
• Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets