Commutativity, Comeasurability, and Contextuality in the Kochen-Specker Arguments

Abstract

I will argue that Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality since, for the argument to be effective, (1) operators must be uniquely associated with measurements and (2) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either 1 or 2 is not met. Arguments meeting 1 contain commuting operators that do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting 2 associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.