The status of determinism in proofs of the impossibility of a noncontextual model of quantum theory

Abstract

In order to claim that one has experimentally tested whether a noncontextual ontological model could underlie certain measurement statistics in quantum theory, it is necessary to have a notion of noncontextuality that applies to unsharp measurements, i.e., those that can only be represented by positive operator-valued measures rather than projection-valued measures. This is because any realistic measurement necessarily has some nonvanishing amount of noise and therefore never achieves the ideal of sharpness. Assuming a generalized notion of noncontextuality that applies to arbitrary experimental procedures, it is shown that the outcome of a measurement depends deterministically on the ontic state of the system being measured if and only if the measurement is sharp. Hence for every unsharp measurement, its outcome necessarily has an indeterministic dependence on the ontic state. We defend this proposal against alternatives. In particular, we demonstrate why considerations parallel to Fine's theorem do not challenge this conclusion.

18 pages. v2 is the published version. Besides the new title, the main change from v1 is the inclusion of a summary of the features of quantum theory that are needed to demonstrate that measurements are represented outcome-deterministically if and only if they are sharp, and why these features by themselves are insufficient to derive a contradiction with noncontextuality

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