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By analogy with the classical conditional entropy, one defines the conditional quantum entropy as <math>S(\rho|\sigma) \equiv S(\rho,\sigma) - S(\sigma)</math>.
An equivalent (and more intuitive) operational definition of the quantum relative entropy (as a measure of the quantum communication cost or surplus when performing quantum state merging) was given by Michal Horodecki, Jonathan Oppenheim, and Andreas Winter in their paper "Quantum Information can be negative" [http://arxiv.org/abs/quant-ph/0505062].
==Properties==
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