On exposed positive maps: Robertson and Breuer-Hall maps

It is well known that so called Breuer-Hall positive maps used in entanglement theory are optimal. We show that these maps possess much more subtle property --- they are exposed. As a byproduct it proves that a Robertson map in the algebra of 4 x 4 complex matrices is not only extreme, which was already shown by Robertson, but also exposed.Comment: 7 page

A Brief History of the GKLS Equation

We reconstruct the chain of events, intuitions and ideas that led to the formulation of the Gorini, Kossakowski, Lindblad and Sudarshan equation.Comment: Based on a talk given by D.C. at the 48th Symposium on Mathematical Physics "Gorini-Kossakowski-Lindblad-Sudarshan Master Equation - 40 Years After" (Toru\'n, June 10-12, 2016). To be published in the special volume of OSI

Circulant states with vanishing quantum discord

We analyze a class of 2-qudit circulant states. They define generalization of well known 2-qubit X-states. We formula the necessary and sufficient criteria for vanishing quantum discord. We illustrate our analysis by an important subclass of circulant states -- so called Bell diagonal states.Comment: 8 page