Uncertainty relation of mixed states by means of Wigner-Yanase-Dyson information

TL;DR

This paper introduces a new, generalized uncertainty relation for mixed quantum states using Wigner-Yanase-Dyson information, extending previous work based on skew information to better quantify quantum uncertainty.

Contribution

It presents a novel uncertainty relation for mixed states utilizing Wigner-Yanase-Dyson information, generalizing prior skew information-based results.

Findings

Derived a generalized uncertainty relation for mixed states

Extended the framework of quantum uncertainty quantification

Provided theoretical insights into quantum and classical uncertainties

Abstract

The variance of an observable in a quantum state is usually used to describe Heisenberg uncertainty relation. For mixed states, the variance includes quantum uncertainty and classical uncertainty. By means of the skew information and the decomposition of the variance, a stronger uncertainty relation was presented by Luo in [Phys. Rev. A 72, 042110 (2005)]. In this paper, by using Wigner-Yanase-Dyson information which is a generalization of the skew information, we propose a general uncertainty relation of mixed states.