Unital map

In abstract algebra, a unital map on a C*-algebra is a map ϕ which preserves the identity element:

This condition appears often in the context of completely positive maps, especially when they represent quantum operations.

If ϕ is completely positive, it can always be represented as

(The E i are the Kraus operators associated with ϕ ). In this case, the unital condition can be expressed as