Conditional entropic uncertainty relations for Tsallis entropies

TL;DR

This paper derives entanglement-dependent entropic uncertainty relations using Tsallis entropies, extending to mixed states and providing bounds relevant for quantum cryptography.

Contribution

It introduces new entropic uncertainty relations based on Tsallis entropies that depend on entanglement and applies them to quantum cryptography scenarios.

Findings

Derived entanglement-dependent uncertainty relations for Tsallis entropies

Extended results to mixed states using von Neumann entropy properties

Provided a lower bound on extractable key in quantum cryptography

Abstract

The entropic uncertainty relations are a very active field of scientific inquiry. Their applications include quantum cryptography and studies of quantum phenomena such as correlations and non-locality. In this work we find entanglement-dependent entropic uncertainty relations in terms of the Tsallis entropies for states with a fixed amount of entanglement. Our main result is stated as Theorem~\ref{th:bound}. Taking the special case of von Neumann entropy and utilizing the concavity of conditional von Neumann entropies, we extend our result to mixed states. Finally we provide a lower bound on the amount of extractable key in a quantum cryptographic scenario.