Mixed-state quantum geometry of dense two-color QCD matter

We investigate an information-geometric approach to dense two-color QCD using thermal states defined as normalized Gibbs states in the two-flavor Nambu–Jona-Lasinio model at the mean-field level. The Bures metric and quantum Fisher information are constructed from thermal states associated with effective Bogoliubov–de Gennes Hamiltonians reproducing the mean-field quasiparticle spectrum. On the thermodynamic parameter manifold $(T,\mu )$, where $T$ is temperature and $\mu$ is quark chemical potential, we analyze information-geometric quantities including the trace of the QFI matrix and the metric-volume density. The numerical results show pronounced enhancements of both quantities near the color-superconducting phase boundary, whereas only weaker signatures are observed across the chiral crossover. By contrast, neither observable exhibits a distinct feature associated with the BEC–BCS crossover.