Conditional Quantum Entropy - Definition

Definition

Given a bipartite quantum state, the entropy of the entire system is, and the entropies of the subsystems are and . The von Neumann entropy measures how uncertain we are about the value of the state; how much the state is a mixed state.

By analogy with the classical conditional entropy, one defines the conditional quantum entropy as .

An equivalent (and more intuitive) operational definition of the quantum conditional entropy (as a measure of the quantum communication cost or surplus when performing quantum state merging) was given by Michał Horodecki, Jonathan Oppenheim, and Andreas Winter in their paper "Quantum Information can be negative" .

Read more about this topic:  Conditional Quantum Entropy

Famous quotes containing the word definition:

    It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.
    François, Duc De La Rochefoucauld (1613–1680)

    ... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.
    George Eliot [Mary Ann (or Marian)

    Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.
    Elaine Heffner (20th century)