Formulation
In the case of a unital C*-algebra, the result is as follows:
Theorem. Let A be a unital C*-algebra, H be a Hilbert space, and B(H) be the bounded operators on H. For every completely positive
there exists a Hilbert space K and a unital *-homomorphism
such that
where is a bounded operator. Furthermore, we have
Informally, one can say that every completely positive map Φ can be "lifted" up to a map of the form .
The converse of the theorem is true trivially. So Stinespring's result classifies completely positive maps.
Read more about this topic: Stinespring Factorization Theorem
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