  We investigate probing the hot and dense nuclear matter with strange vector
mesons ($K^*, \bar{K}^*$). Our analysis is based on PHSD which incorporates
partonic and hadronic dof and describes the full dynamics of HICs. This allows
to study the $K^*$ and $\bar{K}^*$ meson formation from the QGP and the
in-medium effects related to the modification of their properties during the
propagation in dense and hot matter. We employ relativistic Breit-Wigner
spectral functions for the $K^*,\bar{K}^*$ mesons with self-energies obtained
from a G-matrix approach to study the role of in-medium effects on the $K^*$
and $\bar{K}^*$ meson dynamics in HIC from FAIR/NICA to LHC energies. According
to our analysis most of the final $K^*/\bar{K}^*$s, that can be observed
experimentally, are produced during the late hadronic phase and stem dominantly
from the $K (\bar{K}) + \pi \to K^*(\bar{K}^*)$ formation channel. The amount
of $K^*/\bar{K}^*$s originating from the QGP channel is comparatively small
even at LHC energies and such $K^*/\bar{K}^*$s can hardly be reconstructed
experimentally due to the rescattering of final pions and (anti-)kaons. This
mirrors the results from our previous study on the strange vector-meson
production in HICs at RHIC energies. The influence of the in-medium effects on
the dynamics of the $K^*/\bar{K}^*$ is rather small since they are mostly
produced at low baryon densities. Additional cuts on the shape of the observed
signal and the range of the invariant mass region of the $K^*/\bar{K}^*$ also
affect the final spectra. We demonstrate that the $K^*/\bar{K}^*$ in-medium
effects are more visible at lower beam energy, e.g. FAIR/NICA and BES RHIC
energies, where the production of $K^*/\bar{K}^*$s occurs at larger baryon
densities. Finally, we present the experimental procedures to extract
information on the in-medium masses and widths by fitting final mass spectra at
LHC energies.
