  Measurements with variable system-detector interaction strength, ranging from
weak to strong, have been recently reported in a number of electronic
nanosystems. In several such instances many-body effects play a significant
role. Here we consider the weak--to--strong crossover for a setup consisting of
an electronic Mach-Zehnder interferometer, where a second interferometer is
employed as a detector. In the context of a conditional which-path protocol, we
define a generalized conditional value (GCV), and determine its full crossover
between the regimes of weak and strong (projective) measurement. We find that
the GCV has an oscillatory dependence on the system-detector interaction
strength. These oscillations are a genuine many-body effect, and can be
experimentally observed through the voltage dependence of cross current
correlations.
