Crossover between strong and weak measurement in interacting many-body systems

Measurements with variable system–detector interaction strength, ranging from weak to strong, havebeen recently reported in a number of electronic nanosystems. In several such instances many-bodyeffects play a significant role. Here we consider the weak-to-strong crossover for a setup consisting ofan 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.Wefind 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 thevoltage dependence of cross current correlations.