  The connection between the Leggett-Garg inequality and optimal scenarios from
the point of view of quantum metrology is investigated for perfect and noisy
general dichotomic measurements. In this context, we show that the Fisher
information can be expressed in terms of quantum temporal correlations. This
connection allows us to associate scenarios with relatively high Fisher
information to scenarios in which the Leggett-Garg inequality is violated. We
thus demonstrate a qualitative and, to some extent, quantitative link between
measurement invasiveness and metrological performance. Finally, we illustrate
our results by using a specific model for spin systems.
