We prove that the quantum relative entropy decreases monotonically under the application
of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This …

A bstract Tomita-Takesaki modular theory provides a set of algebraic tools in quantum field
theory that is suitable for the study of the information-theoretic properties of states. For every …

After I wrote in 1981 the joint paper [61] with M. Tsukada and M. Ohya on sufficiency of von
Neumann subalgebras and the relative entropy in a specialized situation, I wanted to extend …

We prove the existence of a universal recovery channel that approximately recovers states
on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed …

We give systematic ways of defining monotone quantum relative entropies and (multi-
variate) quantum Rényi divergences starting from a set of monotone quantum relative …

We propose an extension of the sandwiched Rényi relative α α-entropy to normal positive
functionals on arbitrary von Neumann algebras, for the values α> 1 α> 1. For this, we use …

The logarithmic negativity of a bipartite quantum state is a widely employed entanglement
measure in quantum information theory due to the fact that it is easy to compute and serves …

The main result in this paper shows that the quantum f-divergence of two states is equal to
the classical f-divergence of the corresponding Nussbaum–Szkoła distributions. This …

We revisit the connection between index and relative entropy for an inclusion of finite von
Neumann algebras. We observe that the Pimsner–Popa index connects to sandwiched p …

We make a systematic study of standard f-divergences in general von Neumann algebras.
An important ingredient of our study is to extend Kosaki's variational expression of the …