Improved quantum entropic uncertainty relations

TL;DR

This paper develops improved entropic uncertainty relations using linear and quadratic functions, providing tighter bounds for qubit and qutrit systems, including cases with quantum memory, outperforming previous bounds.

Contribution

Introduces new state-independent and state-dependent entropic uncertainty bounds using novel mathematical techniques for quantum systems.

Findings

Derived explicit bounds for qubit and qutrit systems.

Demonstrated bounds outperform existing uncertainty relations.

Extended analysis to systems with quantum memory.

Abstract

We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and the tighter state-dependent one based on the majorization techniques. The analytical results for qubit and qutrit systems with two or three measurement settings are explicitly derived, with detailed examples showing that they outperform the existing bounds. The case with the presence of quantum memory is also investigated.