  In this series of papers, we investigate the projective framework initiated
by Jerzy Kijowski and Andrzej Oko{\l}\'ow, which describes the states of a
quantum theory as projective families of density matrices. After discussing the
formalism at the classical level in a first paper, the present second paper is
devoted to the quantum theory. In particular, we inspect in detail how such
quantum projective state spaces relate to inductive limit Hilbert spaces and to
infinite tensor product constructions. Regarding the quantization of classical
projective structures into quantum ones, we extend the results by Oko{\l}\'ow
[Oko{\l}\'ow 2013, arXiv:1304.6330], that were set up in the context of linear
configuration spaces, to configuration spaces given by simply-connected Lie
groups, and to holomorphic quantization of complex phase spaces.
