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Given two quantum states <math>\rho</math> and <math>\sigma</math>, the von Neumann entropies are <math>S(\rho)</math> and <math>S(\sigma)</math>. The von Neumann entropy measures how uncertain we are about the value of the state; how much the state is a [[mixed state]]. The [[joint quantum entropy]] <math>S(\rho,\sigma)</math> measures our uncertainty about the [[joint system]] which contains both states.
By analogy with the classical conditional entropy, one defines the conditional quantum entropy as <math>S(\rho|\sigma) \
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 [[Michal Horodecki]], [[Jonathan Oppenheim]], and [[Andreas Winter]] in their paper "Quantum Information can be negative" [http://arxiv.org/abs/quant-ph/0505062].
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