Uncertainty relation based on Wigner-Yanase-Dyson skew information with quantum memory

TL;DR

This paper develops new uncertainty relations using Wigner-Yanase-Dyson skew information that incorporate quantum memory, providing bounds that reflect measurement compatibility and quantum correlations, with applications to various quantum states.

Contribution

It introduces novel uncertainty inequalities based on skew information that explicitly include quantum memory effects, advancing understanding of measurement uncertainty in quantum systems.

Findings

Lower bounds depend on measurement compatibility and quantum correlations.

Derived inequalities apply to product, separable, and entangled states.

Examples demonstrate the bounds' effectiveness across different quantum states.

Abstract

We present uncertainty relations based on Wigner--Yanase--Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. \mbox{It is} shown that the lower bounds contain two terms: one characterizes the degree of compatibility of two measurements, and the other is the quantum correlation between the measured system and the quantum memory. Detailed examples are given for product, separable and entangled states.