  A start is made to redefining the topology of the spaces of normal states
(density operators) by a new norm which is finite only for states of finite
entropy. It is shown that a symmetrized version of the free energy difference
between states can be used as a quantum version of the cosh Young function used
in the theory of Orlicz space. The results form a quantum version of the
classical treatment of nonparametric estimation by information geometry, in the
work of Pistone and Sempi. We succeed in constructing the Luxemburg norm, the
tangent space carrying the (+1)-affine structure, and the cotangent space
carrying the (-1) affine structure, and we demonstrate the Holder-Orlicz
inequality.
