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We investigate Leggett-Garg temporal inequalities in flavor-mixing processes.We derive an exact flavor-mass uncertainty product and we establish that it isan upper bound to the violation of the inequalities. This finding relatestemporal nonclassicality to quantum uncertainty and provides a time analog ofthe Tsirelson upper bound to the violation of the spatial Bell inequalities. Bystudying the problem both in the exact field-theoretical setting and in thelimiting quantum mechanical approximation, we show that Leggett-Garginequalities are violated more strongly in quantum field theory than in quantummechanics.

Leggett-Garg inequalities in the quantum field theory of neutrino oscillations