Quantum Relative Entropy - Relation To Other Quantum Information Quantities

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:

    “... a worker was seldom so much annoyed by what he got as by what he got in relation to his fellow workers.”
    —Mary Barnett Gilson (1877–?)

    “There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
    —Adrienne Rich (b. 1929)

    “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)

    “English literature is a kind of training in social ethics.... English trains you to handle a body of information in a way that is conducive to action.”
    —Marilyn Butler (b. 1937)

    “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)