# The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski-Moriya interaction

## TL;DR

This paper investigates how mixedness and entanglement influence the entropic uncertainty in a Heisenberg model with Dzyaloshinski-Moriya interaction, revealing that mixedness better reflects uncertainty and affects its tightness.

## Contribution

It introduces a detailed analysis of the roles of mixedness and entanglement on entropic uncertainty, including a functional relation with magnetic properties and DM interaction.

## Key findings

- Mixedness better reflects entropic uncertainty than entanglement.
- Entanglement reduces the tightness of the uncertainty, while mixedness enhances it.
- The tightness depends on magnetic properties, DM interaction strength, and mixedness, independent of temperature.

## Abstract

The effects of mixedness and entanglement on the lower bound and tightness of the entropic uncertainty in the Heisenberg model with Dzyaloshinski-Moriya (DM) interaction have been investigated. It is found that the mixedness can reflect the essence of the entropic uncertainty better than the entanglement. Meanwhile, the uncertainty of measurement results will be reduced by the entanglement and improved by the mixedness.The entanglement can destroy the tightness of the uncertainty, while the tightness will be improved with the increasing of the mixedness. In addition, the tightness of the uncertainty in Heisenberg model can be expressed as a function of the magnetic properties, the strength of the DM interaction as well as the mixedness of the state and the functional form has no relationship with temperature. What's more, the entropic uncertain inequality becomes uncertain equality when the mixedness of the system reach the minimum value.For a given mixedness, the tightness will be reduced with the increasing of the strength of DM interaction at the antiferromagnetic case while the situation is just the opposite for the ferromagnetic case.

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Source: https://tomesphere.com/paper/1702.04453