Operations and measurements. II

K. -E. Hellwig, K. Kraus

Gábor Hofer‐Szabó

If noncontextuality is defined as the robustness of a system's response to a measurement against other simultaneous measurements, then the Kochen-Specker arguments do not provide an algebraic proof for quantum contextuality. Namely, for the argument to be effective, (i) each operator must be uniquely associated with a measurement and (ii) commuting operators must represent simultaneous measurements. However, in all Kochen-Specker arguments discussed in the literature either (i) or (ii) is not met. Arguments meeting (i) contain at least one subset of mutually commuting operators which do not represent simultaneous measurements and hence fail to physically justify the functional composition principle. Arguments meeting (ii) associate some operators with more than one measurement and hence need to invoke an extra assumption different from noncontextuality.

Gábor Hofer‐Szabó

I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements: (i) each operator is uniquely realized by a single physical measurement; (ii) commuting operators are realized by simultaneous measurements. To underpin this claim, I will construct three hidden variable models for three different physical realizations of the Peres-Mermin square: one violating (i), another violating (ii), and a third one violating both (i) and (ii).

John Earman, Abner Shimony

Bernard d’Espagnat

シロウ イシカワ, Shiro Ishikawa, 史郎 石川

6.1 Regression analysis I 6.2 Bayes operator, Schrödinger picture, and S-states 6.3 Regression analysis II in measurements 6.4 Conclusions