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.
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