Abstract
It is shown that theoretically viable noncontextual hidden-variable models in $d=2$ lead to conflicting dispersion-free expressions in the analysis of the conditional measurement of two non-orthogonal projectors. No satisfactory criterion of the quantum discord, which relies on the analysis of conditional measurement, is formulated in the $d=2$ hidden-variable space due to a lack of uniqueness of the dispersion-free representation. We also make a speculative comment on a ``many-worlds interpretation'' of hidden-variable models to account for the conditional measurement.
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