Conditional quantum entropy: Difference between revisions

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== Definition ==

Given a bipartite quantum state <math>\rho^{AB}</math>, the entropy of the joint system AB is <math>S(AB)_\rho \ \stackrel{\mathrm{def}}{=}\ S(\rho^{AB})</math>, and the entropies of the subsystems are <math>S(A)_\rho \ \stackrel{\mathrm{def}}{=}\ S(\rho^A) = S(\mathrm{tr}_B_A\rho^{AB})</math> and <math>S(B)_\rho</math>. The von Neumann entropy measures an observer's uncertainty about the value of the state, that is, how much the state is a [[mixed state (physics)|mixed state]].

By analogy with the classical conditional entropy, one defines the conditional quantum entropy as <math>S(A|B)_\rho \ \stackrel{\mathrm{def}}{=}\ S(AB)_\rho - S(B)_\rho</math>.