  In this work, we review different generalizations of the quantum geometric
tensor (QGT) in two-band non-Hermitian systems and propose a protocol for
measuring them in experiments. We present the generalized QGT components, i.e.
the quantum metric and Berry curvature, for a non-Hermitian hybrid photonic
(exciton-polariton) system and show that the generalized non-Hermitian QGT can
be constructed from experimental observables. In particular, we extend the
existing method of measuring the QGT that uses the pseudospins in photonic and
exciton-polariton systems by suggesting a method to construct the left
eigenstates from experiments. We also show that the QGT components have clear
signatures in wave-packet dynamics, where the anomalous Hall drift arises from
both the non-Hermitian Berry curvature and Berry connection, suggesting that
both left and right eigenstates are necessary for defining non-Hermitian band
geometries and topologies.
