Weakly sufficient quantum statistics

TL;DR

This paper explores the concept of weak sufficiency in quantum statistics, providing conditions for its existence, examining minimality, and relating it to other sufficiency notions in quantum theory.

Contribution

It offers new necessary and sufficient conditions for weak sufficiency, analyzes minimality, and clarifies its relation to existing sufficiency concepts.

Findings

Established criteria for the existence of weakly sufficient statistics.

Analyzed the minimality conditions for weak sufficiency.

Clarified the relationship between weak sufficiency and other sufficiency notions.

Abstract

Some aspects of weak sufficiency of quantum statistics are investigated. In particular, we give necessary and sufficient conditions for the existence of a weakly sufficient statistic for a given family of vector states, investigate the problem of its minimality, and find the relation between weak sufficiency and other notions of sufficiency employed so far.