Properties of the functional of entropy production for the GKSL equation in theory of open quantum systems and similar problems of quantum cryptography

The talk will be devoted to the functional of entropy production for the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation in theory of open quantum systems. The main property of this functional is its non-negativity. We will talk about a decomposition of this functional into the adiabatic and non-adiabatic components, which are non-negative individually. As an application of this functional, a necessary and sufficient condition for a given density operator to a stationary solution of a given GKSL equation (from a certain class) as well as corresponding examples will be given. Also we will talk about solution of a similar problem in quantum cryptography - namely, a problem of minimization of quantum relative entropy of coherence with linear restrictions.