In abstract algebra

Abstract algebra

Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

, 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 operation

Quantum operation

In quantum mechanics, a quantum operation is a mathematical formalism used to describe a broad class of transformations that a quantum mechanical system can undergo. This was first discussed as a general stochastic transformation for a density matrix by George Sudarshan...

s.

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