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:
“Much poetry seems to be aware of its situation in time and of its relation to the metronome, the clock, and the calendar. ... The season or month is there to be felt; the day is there to be seized. Poems beginning “When” are much more numerous than those beginning “Where” of “If.” As the meter is running, the recurrent message tapped out by the passing of measured time is mortality.”
—William Harmon (b. 1938)
“There is a constant in the average American imagination and taste, for which the past must be preserved and celebrated in full-scale authentic copy; a philosophy of immortality as duplication. It dominates the relation with the self, with the past, not infrequently with the present, always with History and, even, with the European tradition.”
—Umberto Eco (b. 1932)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“Information networks straddle the world. Nothing remains concealed. But the sheer volume of information dissolves the information. We are unable to take it all in.”
—Günther Grass (b. 1927)
“Compilers resemble gluttonous eaters who devour excessive quantities of healthy food just to excrete them as refuse.”
—Franz Grillparzer (1791–1872)