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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>.
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 [[
==Properties==
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