Entropic Uncertainty Principle and Information Exclusion Principle for multiple measurements in the presence of quantum memory

TL;DR

This paper derives tighter bounds on entropic uncertainty and information exclusion principles for multiple measurements with quantum memory, demonstrating their application on Werner and bound entangled states.

Contribution

It introduces improved bounds for multiple measurements in quantum systems with memory, extending previous uncertainty relations.

Findings

Tighter bounds on entropic uncertainty relations.

Application to Werner and bound entangled states.

Enhanced understanding of measurement incompatibility.

Abstract

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We present tighter bounds on both entropic uncertainty relation and information exclusion principle for multiple measurements in the presence of quantum memory. As applications, three incompatible measurements on Werner state and Horodecki's bound entangled state are investigated in details.