Application
In quantum information theory, quantum channels, or quantum operations, are defined to be completely positive maps between C*-algebras. Being a classification for all such maps, Stinespring's theorem is important in that context. For example, the uniqueness part of the theorem has been used to classify certain classes of quantum channels.
For the comparison of different channels and computation of their mutual fidelities and information another representation of the channels by their "Radon-Nikodym" derivatives introduced by Belavkin is useful. In the finite dimensional case, Choi's theorem as the tracial variant of the Belavkin's Radon-Nikodym theorem for completely positive maps is also relevant. The operators from the expression
are called the Kraus operators of Φ. The expression
is sometimes called the operator sum representation of Φ.
Read more about this topic: Stinespring Factorization Theorem
Famous quotes containing the word application:
“Most people, no doubt, when they espouse human rights, make their own mental reservations about the proper application of the word “human.””
—Suzanne Lafollette (1893–1983)
“The human mind is capable of excitement without the application of gross and violent stimulants; and he must have a very faint perception of its beauty and dignity who does not know this.”
—William Wordsworth (1770–1850)
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)