Uncertainty Relations from Simple Entropic Properties

Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and as well as being fundamental to our understanding of quantum theory, they have practical applications such as for cryptography and witnessing entanglement. Here we shed new light on the entropic form of these relations, showing that they follow from a few simple properties, including the data-processing inequality. We prove these relations without relying on the exact expression for the entropy, and hence show that a single technique applies to several entropic quantities, including the von Neumann entropy, min- and max-entropies, and the Rényi entropies.