Reply to Pavici\'c's 'Comment on "Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies"' (arXiv:2502.13787)
Abstract
According to Pavici\'c, Kochen and Specker's 117-observable set is not a ``Kochen-Specker set''. By the same reason, in arXiv:2502.13787, Pavici\'c claims that 10 statements in our paper ``Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies'' [Phys. Rev. A 111, 022408 (2025)] are ``wrong''. In all cases, Pavici\'c's claims are based on the fact that he is assuming a different definition of Kochen-Specker (KS) set. Adopting a terminology used by, e.g., Larsson, the sets that Pavici\'c call KS sets can be called ``extended'' KS sets, since they are constructed by adding observables to the ``original'' KS sets. For example, Pavici\'c adds 75 observables to the original 117-observable KS set. Beyond terminology, there are fundamental physical reasons for focusing on the original KS sets. One reason is that, for experimentally observing quantum state-independent contextuality, there is no need to measure the observables added in the extended sets. Another reason is that, to produce bipartite perfect quantum strategies, or correlations in a face of the nonsignaling polytope with no local points, or correlations with nonlocal content 1, the two parties do not need to measure any of the observables added in the extended sets. We also respond to other claims made by Pavici\'c about our work.
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