Relation To Other Quantum Information Quantities
One reason the quantum relative entropy is useful is that several other important quantum information quantities are special cases of it. Often, theorems are stated in terms of the quantum relative entropy, which lead to immediate corollaries concerning the other quantities. Below, we list some of these relations.
Let ρAB be the joint state of a bipartite system with subsystem A of dimension nA and B of dimension nB. Let ρA, ρB be the respective reduced states, and IA, IB the respective identities. The maximally mixed states are IA/nA and IB/nB. Then it is possible to show with direct computation that
where I(A:B) is the quantum mutual information and S(B|A) is the quantum conditional entropy.
Read more about this topic: Quantum Relative Entropy
Famous quotes containing the words relation to, relation, quantum, information and/or quantities:
“The adolescent does not develop her identity and individuality by moving outside her family. She is not triggered by some magic unconscious dynamic whereby she rejects her family in favour of her peers or of a larger society.... She continues to develop in relation to her parents. Her mother continues to have more influence over her than either her father or her friends.”
—Terri Apter (20th century)
“The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.”
—Sigmund Freud (1856–1939)
“The receipt to make a speaker, and an applauded one too, is short and easy.—Take of common sense quantum sufficit, add a little application to the rules and orders of the House, throw obvious thoughts in a new light, and make up the whole with a large quantity of purity, correctness, and elegancy of style.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“So while it is true that children are exposed to more information and a greater variety of experiences than were children of the past, it does not follow that they automatically become more sophisticated. We always know much more than we understand, and with the torrent of information to which young people are exposed, the gap between knowing and understanding, between experience and learning, has become even greater than it was in the past.”
—David Elkind (20th century)
“James Brown and Frank Sinatra are two different quantities in the universe. They represent two different experiences of the world.”
—Imamu Amiri Baraka [Everett Leroi Jones] (b. 1934)