Contextuality analysis of disturbing data cannot preserve core Kochen-Specker principles
arXiv:2212.06976
Abstract
We address the challenge of extending the criterion for Kochen-Specker contextuality to data with disturbance, to accommodate experimental imperfections or applications to macroscopic settings beyond quantum physics. We find that any such extension must abandon one or more principles that are core to the concept of contextuality. Specifically, we prove that no extended criterion agreeing with Kochen-Specker contextuality in the absence of disturbance can simultaneously satisfy the following: (1) any deterministic system is noncontextual; (2) discarding information cannot turn a noncontextual system into a contextual one; (3) classical post-processing cannot create contextuality; and (4) the joint realization of two statistically independent noncontextual systems is noncontextual. From the standpoint of resource theories, the obstruction arises because free operations can turn noncontextual disturbing behaviors into contextual non-disturbing ones. We suggest that future work on extended contextuality needs to move beyond the standard model-independent framework and account for the causal structure responsible for disturbance.
arXiv comment9 pages