We introduce a generalization of relative entropy derived from the WignerYanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint… (More)

This paper attempts to develop a theory of sufficiency in the setting of non-commutative algebras parallel to the ideas in classical mathematical statistics. Sufficiency of a coarse-graining means… (More)

We present a construction of a Banach manifold on the set of faithful normal states of a von Neumann algebra, where the underlying Banach space is a quantum analogue of an Orlicz space. On the… (More)

We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2-sufficient for a pair of states {ρ 0 , ρ 1 } if it contains all Bayes optimal tests of ρ 0 against ρ 1. In… (More)

On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using… (More)

This paper attempts to give an overview about sufficiency in the setting of quantum statistics. The basic concepts are treated paralelly to the the measure theoretic case. It turns out that several… (More)

For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by post-processings of the other channel can be characterized by comparing the… (More)

For a pair of quantum channels with the same input space, we show that the possibility of approximation of one channel by postprocessings of the other can be characterized by comparing the success… (More)

The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The… (More)