Unital map

In abstract algebra, a unital map on a C*-algebra is a map ϕ {displaystyle phi } which preserves the identity element: In abstract algebra, a unital map on a C*-algebra is a map ϕ {displaystyle phi } which preserves the identity element: This condition appears often in the context of completely positive maps, especially when they represent quantum operations. If ϕ {displaystyle phi } is completely positive, it can always be represented as (The E i {displaystyle E_{i}} are the Kraus operators associated with ϕ {displaystyle phi } ). In this case, the unital condition can be expressed as