'''Strong sub-additivity''' is a relationship between various entropic quantities. In [[quantum information theory, it gives
S(AB)+S(BC)\geq S(ABC)+S(B)
One can write it suggestively in terms of the [[conditional entropy]] as
S(A|BC)\leq S(A|B)
where it follows from the fact that the rate of [[quantum state merging]] can only be better if the receiver has access
to additional information.
Strong sub-additivity implies [[sub-additivity]], namely that , which is another way of saying
that the [[quantum mutual information]] is always positive. To see this result, just make the state on system "B" pure.
Currently, it is open problem to find non-constrained inequalities among entropies which are not implied by
strong subadditivity.
It is of interest which states saturate the strong sub-additivty bound.
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[[Category:Quantum Information Theory]]
[[Category:Handbook of Quantum Information]]
