Uncertainty principle for Wigner-Yanase-Dyson information in semifinite von Neumann algebras

TL;DR

This paper extends an uncertainty principle related to Wigner-Yanase-Dyson information from matrices to the more general setting of semifinite von Neumann algebras, broadening its mathematical scope.

Contribution

The paper proves a new uncertainty principle for Wigner-Yanase-Dyson information within semifinite von Neumann algebras, addressing a question posed by Kosaki.

Findings

Established an uncertainty inequality in semifinite von Neumann algebras.

Extended matrix-based uncertainty principles to operator algebra setting.

Provided a mathematical foundation for future quantum information research.

Abstract

Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty principle in the semifinite case.