Appears in collection : 2017 - T3 - WS2 - Probabilistic techniques and quantum information theory

I will discuss recent results concerning almost optimal entropic and metric (total-variation and Hellinger) uncertainty relations which hold with high probability for measurements given by i. i. d. Haar distributed random unitary matrices. If time permits I will also discuss some applications to information locking and data hiding. The talk will be partially based on joint work with Rafal Latala, Zbigniew Puchala and Karol Zyczkowski.