**5. Discussion**

Currently, 'time' does not play any essential role in quantum information theory. In this sense, quantum theory is underdeveloped similarly to how quantum physics was underdeveloped before Schrödinger introduced his wave equation. In this review article, we discussed a fascinating extension of the Keldysh formalism that consistently copes with the problem of time for one of the central quantities in quantum information theory: entropy. We characterized the flows of conserved entropies (both Renyi and von Neumann entropies) and illustrated them diagrammatically to introduce new correlators that have been absent so far in the literature.

Given that entropy is not an observable, as it is a nonlinear function of the density matrix, one can use a probe environment to make an indirect measurement of the entropy in light of the new correspondence between entropy and full counting statistics of energy transfer. This can be done equally well for the imaginary and real values of the characteristic parameter. The measurement procedures may be complex, ye<sup>t</sup> they are feasible and physical. The correspondence can have many other advantages. For instance, a complete understanding of entropy flows may help to identify the sources of fidelity loss in quantum communication and may help to develop methods to control or even prevent them.

**Author Contributions:** Y.V.N. contributed in conceptualization and idea; A.v.S. in editing, and M.H.A. wrote the original draft.

**Funding:** The authors declare no funding support.

**Conflicts of Interest:** The authors declare no conflict of interest.
