The set of states modelled on an Orlicz space

by R. F. Streater, to appear in the proceedings of the conference on quantum information in honour of R. L. Hudson, Nottingham, July 2006. Editor: M. Guta.

We give an account of the development of the quantum version of the theory of Pistone and Sempi, who developed a theory of estimation in classical statistical theory; the theory of Young functions, Orlicz spaces and the work of Pistone and Sempi is briefly described.

The main difference with previous attempts in this direction is in the choice of quantum Young function. This is taken to be the function 1/2(Z(H + X) + Z(H-X)) - 1 , where Z(H) is the partition function, regarded as a function of the perturbation X of the total energy H + X from the energy H . The theory covers the case where X is an H-small form.