Transformations of Classical and Quantum States and Discrete Dynamics in Quantum Measurements

This lecture presents "Transformations of classical and quantum states and discrete dynamics in the set of quantum measurements" by Karol Zyczkowski from Jagiellonian University, recorded at IPAM's Dynamics of Density Operators Workshop. Explore the mathematical framework of discrete dynamics in probability vectors and density operators, focusing on generalized measurements (POVM) and their transformations through blockwise stochastic matrices. Learn how these transformations correspond to sequences of quantum measurements and discover a quantum analog of Ostrowski's description of the classical Birkhoff polytope. The presentation introduces the concept of majorization between quantum measurements and provides a dynamical characterization of blockwise bistochastic matrices, sometimes called quantum magic squares. This research represents joint work with Albert Rico, Moises Moran, and Shmuel Fridland.