Weakly sufficient quantum statistics

Abstract

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.

State Determination and Sufficiency of Observables

“…Sufficiency of algebra N for the family of states {ρ θ } was investigated in [7,8] in some special situation i.e. for…”

“…Sufficiency of a quantum statistic in Petz's sense was introduced in [9] (under the name of 'sufficiency'), and afterwards analyzed in [7,8]. State determination and distinction was investigated in [2] and [1].…”

Lüders Instruments, Generalised Lüders Theorem, and Some Aspects of Sufficiency

“…Obviously, sufficiency in Umegaki's sense implies sufficiency in Petz's sense which in turn implies sufficiency. Some aspects of sufficiency, Petz's sufficiency, and Umegaki's sufficiency were investigated in [13], [6,7], and [17,18], respectively, while in [8,9] …”