Genuine Global Kochen-Specker Contextuality as Classical Coordination Cost

Classical simulations of quantum correlations can fail because no low-communication local hidden-variable model exists, or because no single noncontextual hidden state can explain all compatible measurement contexts. This manuscript studies a third regime: genuine global Kochen-Specker contextuality, where local subsystems are noncontextual and the tested multipartite blocks are generalized-Bell-local, but the whole empirical model admits no global noncontextual hidden-variable explanation. We propose a coordination-cost framework in which communication, memory, and local computation are treated as different ways for a classical simulator to maintain a global classical explanation from locally available information. We introduce coordination bits, global contextual covering numbers, scaling laws for task families, and an abstract lifting theorem showing how classical simulation lower bounds for KS-contextual seed families can be transferred to genuinely global-KS models. As worked examples, we analyze a polarization-path Hardy obstruction and postselected KCBS-type tasks.

Source: arXiv:2606.23577v1 - http://arxiv.org/abs/2606.23577v1 PDF: https://arxiv.org/pdf/2606.23577v1 Original Link: http://arxiv.org/abs/2606.23577v1