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:
“Whoever has a keen eye for profits, is blind in relation to his craft.”
—Sophocles (497–406/5 B.C.)
“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)
“As information technology restructures the work situation, it abstracts thought from action.”
—Shoshana Zuboff (b. 1951)
“Compilers resemble gluttonous eaters who devour excessive quantities of healthy food just to excrete them as refuse.”
—Franz Grillparzer (1791–1872)