Dynamics Investigation of the quantum-control-assisted multipartite uncertainty relation in Heisenberg model with Dzyaloshinski-Moriya interaction

TL;DR

This paper explores the dynamics of a multipartite quantum uncertainty relation in a Heisenberg model with Dzyaloshinski-Moriya interaction, revealing a unique relationship between mixedness and the uncertainty bounds.

Contribution

It introduces the analysis of the new quantum-control-assisted uncertainty relation's dynamics in a specific quantum system, highlighting the link between mixedness and uncertainty tightness.

Findings

Mixedness has a single-valued relationship with uncertainty bounds.

The relationship between mixedness and uncertainty is independent of the uncertainty relation form.

Comparison made between variance-based and entropic uncertainty relations.

Abstract

Recently, Zheng constructs a quantum-control-assisted multipartite variance-based uncertainty relation, which successfully extends the conditional uncertainty relation to the multipartite case [Annalen der physik, 533, 2100014 (2021)]. We here investigate the dynamics of the new uncertainty relation in the Heisenberg system with the Dzyaloshinski-Moriya interaction. It is found that, different from entanglement, the mixedness of the system has an interesting single-valued relationship with the tightness and lower bound of the uncertainty relation. This single-valued relationship indicates that the tightness and lower bound of the uncertainty relation can be written as the functional form of the mixedness. Moreover, the single-valued relationship with the mixedness is the common nature of conditional uncertainty relations, and has no relationship with the form of the uncertainty relations. Also, the comparison between the new conditional variance-based uncertainty relation and the existing entropic one has been made.