Completely positive map

In mathematics a positive map is a map between C*-algebras that sends positive elements to positive elements. A completely positive map is one which satisfies a stronger, more robust condition.

Let ${\displaystyle A}$ and ${\displaystyle B}$ be C*-algebras. A linear map ${\displaystyle \phi :A\to B}$ is called positive map if ${\displaystyle \phi }$ maps positive elements to positive elements: ${\displaystyle a\geq 0\implies \phi (a)\geq 0}$.

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