= Solution
For a bipartite <density operator> $\rho_{AB}$, the <Subadditivity of Von Neumann entropy> is
$$
\boxed{S(AB)\leq S(A)+S(B)}.
$$
Here $S(A)=S(\operatorname{Tr}_B\rho_{AB})$ and likewise for $B$, using the <partial trace>. For a tripartite density operator, the <Strong subadditivity of Von Neumann entropy> is
$$
\boxed{S(ABC)+S(B)\leq S(AB)+S(BC)}.
$$
Equivalently, <quantum conditional entropy> cannot increase upon adding a conditioning system: $S(A\mid BC)\leq S(A\mid B)$.
Back to article page
