**6. Conclusions**

This review addressed the importance of interactions for the investigation and control of dynamical quantum coherent phenomena in mesoscopic quantum-dot devices.

In Section 2, we discussed how interactions are the essential ingredient allowing long-range quantum state transfer in mesoscopic devices. Notice that the same phenomenon has been suggested to enforce nonlocal phase-coherent electron transfer in wires supporting topologically protected Majorana modes at their edges [207,208]. Such an effect is currently being considered in various Majorana network models for stabilizer measurements in corresponding implementations of topological quantum error correction codes [209–211].

The local Fermi liquid approach, discussed in Section 3, provides the unifying theoretical framework to describe the low-energy dynamics of such various mesoscopic devices. Its application to the various experimental setups mentioned in the Introduction, will be definitively useful to bring further understanding in the complex and rich field of out-of-equilibrium many-body systems. The insight given on universal quantum dissipation phenomena, discussed for the mesoscopic capacitor in Section 4, and, in particular, the novel interaction effects, unveiled in the experiment discussed in Section 5, give two clear examples of the utility of this approach.

Beyond the already mentioned potential for quantum dot devices coupled to microwave cavities [150–159] and to energy transfer [178–180], important extensions of the LFL approach should be envisioned for understanding the properties of mesoscopic devices involving non-Fermi liquids at the place of normal metallic leads. The most important cases would involve superconductors [18,19,212–217] or fractional Quantum Hall edges states, in which quantum noise measurements have been crucial to address and unveil the dynamics of fractionally charged excitations [218–235]. Additionally, the recent realization of noiseless levitons [8–12] paves the way to interesting perspectives to investigate flying anyons [13,220,236] and novel interesting dynamical effects [188,189,237].

**Author Contributions:** M.F. prepared and finalized the original draft of this review, C.M. gave substantial suggestion for its structure and all the authors equally contributed to revise the manuscript. A.M. and G.F. realized the original data analysis presented in Figure 14. All authors have read and agreed to the published version of the manuscript.

**Funding:** M.F. acknowledges support from the FNS/SNF Ambizione Grant PZ00P2\_174038 and G.F. is funded by ERC consolidator gran<sup>t</sup> "EQuO" (no. 648236).

**Acknowledgments:** M.F. is indebted to Christopher Bäuerle, Géraldine Haack, Frédéric Pierre, Inès Safi, and Eugene Sukhorukov for important comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest. The founders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
