  We first consider a generic two-band model which can be mapped to a
pseudospin on a Bloch sphere. We establish the link between the pseudospin
orientation and the components of the quantum geometric tensor (QGT): the
metric tensor and the Berry curvature. We show how the k-dependent pseudospin
orientation can be measured in photonic systems with radiative modes. We
consider the specific example: a 2D planar cavity with two polarization
eigenmodes, where the pseudospin measurement can be performed via
polarization-resolved photoluminescence. We also consider the s-band of a
staggered honeycomb lattice for polarization-degenerate modes (scalar photons).
The sublattice pseudospin can be measured by performing spatially resolved
interferometric measurements. In the second part, we consider a more
complicated four-band model, which can be mapped to two entangled pseudospins.
We show how the QGT components can be obtained by measuring six angles. The
specific four-band system we considered is the s-band of a honeycomb lattice
for polarized (spinor) photons. We show that all six angles can indeed be
measured in this system. We simulate realistic experimental situations in all
cases. We find the photon eigenstates by solving Schrodinger equation including
pumping and finite lifetime, and then simulate the measurement of the relevant
angles to finally extract realistic mappings of the k-dependent QGT components.
