Modular Deutsch Entropic Uncertainty Principle

TL;DR

This paper extends the Deutsch entropic uncertainty principle to Hilbert C*-modules over commutative unital C*-algebras using the Buzano inequality, broadening the mathematical framework of quantum uncertainty.

Contribution

It introduces a novel derivation of the Deutsch entropic uncertainty principle within the context of Hilbert C*-modules, utilizing the Buzano inequality.

Findings

Derived Deutsch entropic uncertainty principle for Hilbert C*-modules.

Connected Buzano inequality to quantum uncertainty principles.

Extended mathematical framework for quantum information theory.

Abstract

Khosravi, Drnov\v{s}ek and Moslehian [\textit{Filomat, 2012}] derived Buzano inequality for Hilbert C*-modules. Using this inequality we derive Deutsch entropic uncertainty principle for Hilbert C*-modules over commutative unital C*-algebras.