Effects as functions on projective Hilbert space
P. Busch, S.P. Gudder
TL;DR
This paper explores how effect operators in a complex Hilbert space can be represented as functions on one-dimensional projections, analyzing the properties of this mathematical embedding.
Contribution
It introduces and investigates an injective mapping from effect operators to functions on projections, revealing new structural insights.
Findings
The injection is injective, preserving effect operator distinctions.
Properties of the embedding are characterized in detail.
The approach provides a new perspective on effect operators in quantum theory.
Abstract
The set of effect operators in a complex Hilbert space can be injectively embedded into the set of functions from the set of one-dimensional projections to the real interval [0,1]. Properties of this injection are investigated.
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