Review on entropic uncertainty relations

The Heisenberg uncertainty principle is one of the characteristics of quantum mechanics. With the vigorousdevelopment of quantum information theory, uncertain relations have gradually played an important role in it.In particular, in order to solved the shortcomings of the concept in the initial formulation of the uncertaintyprinciple, we brought entropy into the uncertainty relation, after that, the entropic uncertainty relation hasexploited the advantages to the full in various applications. As we all know the entropic uncertainty relationhas became the core element of the security analysis of almost all quantum cryptographic protocols. This reviewmainly introduces development history and latest progress of uncertain relations. After Heisenberg's argumentthat incompatible measurement results are impossible to predict, many scholars, inspired by this viewpoint,have made further relevant investigations. They combined the quantum correlation between the observableobject and its environment, and carried out various generalizations of the uncertainty relation to obtain moregeneral formulas. In addition, it also focuses on the entropy uncertainty relationship and quantum-memory-assisted entropic uncertainty relation, and the dynamic characteristics of uncertainty in some physical systems.Finally, various applications of the entropy uncertainty relationship in the field of quantum information arediscussed, from randomnesss to wave-particle duality to quantum key distribution.