Contextuality is a fundamental feature of quantum mechanics whereby we realize that the measurements we make of a quantum system depend crucially on the context in which we make them. One might hope that there are preexisting parameters with definite values underlying quantum mechanics, which some more fundamental theory could use to explain the measurements we observe. Theorems of Bell, Kochen, and Specker established that this cannot be the case.
Underlying such theorems is a common theme: information available locally (i.e., on restricted contexts) cannot be extended globally. This realization led to a reformulation of contextuality in terms of (pre)sheaves, a mathematical tool capturing the essence of such local-global problems. In this talk, we will overview this sheaf theoretic treatment of contextuality. Presheaves defined over the commutative subalgebras of a C*-Algebra play a central role. We reformulate the Kochen-Specker theorem, the original inspiration for this approach. We also view the broader idea of sheaf-theoretic contextuality from this setting, including the connection to sheaf cohomology and topos theory.
Meeting ID: 940 0255 3301 Passcode: 790356
The Sheaf Theoretic Approach to Contextuality in Quantum Mechanics