Foundations of Physics 44 (11):1125-1155 (2014)

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
Keywords Quantum contextuality  Kochen–Specker theorem  Quantum foundations  Positive operator valued measures  Quantum measurement theory
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DOI 10.1007/s10701-014-9833-x
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References found in this work BETA

The Problem of Hidden Variables in Quantum Mechanics.Simon Kochen & E. P. Specker - 1967 - Journal of Mathematics and Mechanics 17:59--87.

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