Uncertainty relations from simple entropic properties

TL;DR

This paper demonstrates that fundamental quantum uncertainty relations can be derived from basic entropic properties like data processing inequality, applying to various entropies without relying on their explicit formulas.

Contribution

It introduces a unified method to derive entropic uncertainty relations from simple properties, broadening their applicability across different entropy measures.

Findings

Uncertainty relations follow from basic entropic properties.

The approach applies to von Neumann, min-, max-, and Renyi entropies.

The derivation does not depend on explicit entropy formulas.

Abstract

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 entropic 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 Renyi entropies.