Choi's theorem on completely positive maps, proved by Man-Duen Choi in 1975, classifies the completely positive linear maps between finite-dimensional matrix C*-algebras. It shows that every such map can be built from a finite set of matrices in a specific decomposed form, giving a concrete structural description of maps that are central to operator algebra's own study and, later, to quantum information theory, where completely positive maps model the most general physically allowed evolution of a quantum state. An infinite-dimensional generalization of the theorem is known as Belavkin's Radon-Nikodym theorem for completely positive maps.
Facts
StatementClassifies completely positive maps between finite-dimensional (matrix) C*-algebras. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Choi's theorem on completely positive maps - Wikipedia
Intro, first sentence
a result that classifies completely positive maps between finite-dimensional (matrix) C*-algebras
Intro, second sentence
This 1975 theorem is due to Man-Duen Choi.
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.