Noninvasive Quantum Measurement of Arbitrary Operator Order in a Mesoscopic Double-Dot Detector Setup

The development of solid-state quantum technologies requires the understanding of quantum measurements in interacting, non-isolated systems. Historically the interpretation of quantum measurement uses the projection postulate implying an instantaneous collapse of the wave function. In many real systems the interaction is much weaker and a collapse is avoided which is crucial to observe non-commuting observables simultaneously.

Our goal is to understand which system correlations are obtained in a generalized quantum measurement. We analyze a generic setup of two independent detectors coupled to a quantum system and derive a compact formula in the weak-measurement limit. For an almost continuous measurement, understanding the detector dynamics becomes an important issue as the result will dependent on the detectors memory and the cross-talk between the detectors through the system.
Based on our findings we propose a mesoscopic double-dot detector setup in which the memory effect is tunable to explore the transition to non-Markovian quantum measurements experimentally. Going beyond the usually discussed bath-induced non-Markovian self-interaction, we identify the system-mediated detector-detector interaction as crucial ingredient to explore non-Markovian quantum measurements.