Dynamic Investigation of the New Quantum-Control-Assisted Reverse uncertainty relation

TL;DR

This paper introduces a quantum-control-assisted reverse uncertainty relation, explores its dynamic evolution in a Heisenberg model, and reveals a relationship between uncertainty and system mixedness, expanding understanding of quantum uncertainties.

Contribution

It constructs a new reverse uncertainty relation aided by quantum control and investigates its dynamics, highlighting the link between uncertainty bounds and system mixedness.

Findings

Reverse uncertainty can be broken with quantum control.

Uncertainty bounds relate to the mixedness of the quantum state.

The relationship between uncertainty and mixedness is common to both normal and reverse relations.

Abstract

Recently, a new interesting concept of reverse uncertainty relation is introduced. Different from the normal uncertainty relation, the reverse one indicates that one cannot only prepare quantum states with joint small uncertainty, but also with joint great uncertainty for incompatible observables. We in this work construct a new quantum-control-assisted reverse uncertainty relation and investigate the corresponding dynamic evolution in the Heisenberg model with Dzyaloshinskii-Moriya interaction. The obtained relation indicates that the reverse uncertainty can be broken with help of the quantum control system. The dynamic investigation reveals that there exists an interesting single-value relationship between new uncertainty relation and the mixedness of the system, indicating that the tightness and upper bound of the uncertainty relation can be written as functional form of the mixedness. By comparing the existing research in [Physica Scripta 2023, 98(6), 065113], we show that the single-value relationship with the mixedness is the common nature of both the normal uncertainty relations and the reverse uncertainty relation.