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Concept# Conditional quantum entropy

Résumé

The conditional quantum entropy is an entropy measure used in quantum information theory. It is a generalization of the conditional entropy of classical information theory. For a bipartite state \rho^{AB}, the conditional entropy is written S(A|B)*\rho, or H(A|B)*\rho, depending on the notation being used for the von Neumann entropy. The quantum conditional entropy was defined in terms of a conditional density operator \rho_{A|B} by Nicolas Cerf and Chris Adami, who showed that quantum conditional entropies can be negative, something that is forbidden in classical physics. The negativity of quantum conditional entropy is a sufficient criterion for quantum non-separability.
In what follows, we use the notation S(\cdot) for the von Neumann entropy, which will simply be called "entropy".
Definition
Given a bipartite quantum state \rho^{AB}, the entropy of the joint system AB is S(AB)_\r

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Von Neumann entropy

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