Berry's phase in view of quantum estimation theory, and its intrinsic relation with the complex structure

TL;DR

This paper explores the connection between Berry's phase, quantum estimation theory, and the complex structure of Hilbert space, highlighting its role as an indicator of non-commutativity in quantum models.

Contribution

It establishes a novel link between Berry's phase and the complex structure in quantum estimation, emphasizing its significance as a measure of non-commutativity.

Findings

Berry's phase indicates the degree of non-commutativity in quantum models

Intrinsic relations between complex structure and Berry's phase are identified

Berry's phase serves as a useful index in quantum statistical models

Abstract

In this paper, it is pointed out that the Berry's phase is a good index of degree of no-commutativity of the quantum statistical model. Intrinsic relations between the `complex structure' of the Hilbert space and Berry's phase is also discussed.