{c}
{wiki=Strong_subadditivity_of_quantum_entropy}

For a tripartite <density operator> $\rho_{ABC}$,
$$
S(\rho_{ABC})+S(\rho_B)\leq S(\rho_{AB})+S(\rho_{BC}).
$$
Equivalently, conditioning on an additional quantum system cannot increase <quantum conditional entropy>.


Strong subadditivity of Von Neumann entropy

The <quantum conditional entropy> has the relative-entropy representation
$$
-H(A|B)_\rho=\min_{\xi_B}D(\rho_{AB}\|I_A\otimes\xi_B),
$$
where the minimum ranges over <density operator>[density operators] on $B$.


Variational characterization of quantum conditional entropy

{title2=$H(A|B)_\rho$}
{wiki}

The quantum conditional entropy is $H(A|B)_\rho=S(\rho_{AB})-S(\rho_B)$. Unlike its classical counterpart, it may be negative.


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 Incoming links: Quantum conditional entropy