Uncertainty and complementarity relations based on generalized skew information

TL;DR

This paper develops new uncertainty and complementarity relations in quantum mechanics using generalized skew information, applicable to various measurement types, and includes specific examples demonstrating their validity.

Contribution

It introduces novel uncertainty and complementarity relations based on generalized skew information for mutually unbiased measurements and SIC-POVMs, extending existing results.

Findings

Derived new uncertainty relations using GWYD skew information.

Established complementarity relations for MUMs and SIC-POVMs.

Provided detailed examples illustrating the theoretical results.

Abstract

Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and complementarity relations with respect to mutually unbiased measurements (MUMs), and general symmetric informationally complete positive operator valued measurements (SIC-POVMs), respectively. Our results include some existing ones as particular cases. We also exemplify our results by providing a detailed example.