Product and sum uncertainty relations based on metric-adjusted skew information

TL;DR

This paper develops new uncertainty relations in quantum mechanics using metric-adjusted skew information, providing lower bounds for product and sum forms and illustrating them with explicit examples.

Contribution

It introduces novel uncertainty bounds based on metric-adjusted skew information, linking quantum geometry and information measures.

Findings

Derived lower bounds for uncertainty relations

Established connections between quantum geometry and information

Validated bounds with explicit examples

Abstract

The metric-adjusted skew information establishes a connection between the geometrical formulation of quantum statistics and the measures of quantum information. We study uncertainty relations in product and summation forms of metric-adjusted skew information. We present lower bounds on product and summation uncertainty inequalities based on metric-adjusted skew information via operator representation of observables. Explicit examples are provided to back our claims.