Short-time-interaction quantum measurement through an incoherent mediator

We develop a theory of indirect measurements where a probe is able to read, in short interaction times, the quantum state of a remote system through an incoherent wall. The probe and the system can interact with an ancilla in an incoherent state but not directly among themselves and, nevertheless, the fast transfer of quantum information can be achieved with robustness. We exemplify our measurement scheme with a paradigmatic example of this tripartite problem: qubit-oscillator-qubit, and discuss different physical scenarios pointing out the associated advantages and limitations.