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For the remainder of the article, we use the notation <math>S(\rho)</math> for the von Neumann entropy.
== Definition ==
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 (physics)|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) \ \stackrel{\mathrm{def}}{=}\ S(\rho,\sigma) - S(\sigma)</math>.
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