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

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

If is completely positive, it can always be represented as

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

- Paulsen, Vern I. (2002).
*Completely bounded maps and operator algebras*. Cambridge: Cambridge University Press. ISBN 0-511-06103-X. OCLC 228110971.