= Quantum conditional entropy
{title2=$H(A|B)_\rho$}
{wiki}
The quantum conditional entropy is $H(A|B)_\rho=S(\rho_{AB})-S(\rho_B)$, with a common logarithm base used in both <Von Neumann entropies>. It compares uncertainty of the joint state with that of the specified subsystem; it is not obtained by assigning classical probabilities to every pair of incompatible quantum measurements.
For a <product state> $\rho_A\otimes\rho_B$, additivity gives $H(A|B)=S(\rho_A)$. For a pure <Bell state>, the joint entropy is zero while either subsystem entropy is one bit, so $H(A|B)=-1$ bit. Negative values have no classical Shannon-entropy counterpart and signal entanglement, although some entangled mixed states have nonnegative conditional entropy. The ordering of $A$ and $B$ matters in general because their marginal entropies can differ.
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