Commit 2025-05-03 14:10 01aca3ad
View on Github →feat(CStarAlgebra): define completely positive maps (#24359)
This PR defines completely positive maps. A linear map φ : A₁ →ₗ[ℂ] A₂
(where A₁
and A₂
are C⋆-algebras) is called completely positive (CP) if applying φ
to all entries of a k × k matrix is also positive for every k ∈ ℕ
.
Here we provide the definition and a few basic properties: CP maps are positive, and non-unital star algebra homomorphisms are CP. A fair amount of supporting material was also added to CStarMatrix
. The API is still very barebones and we leave e.g. composition for subsequent PRs.