Structure of sufficient quantum coarse-grainings
Abstract
Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K). Assume that density matrices D1 and D2 acting on H are given. In the paper the consequences of the existence of a coarse-graining S from B(K) to B(H) satisfying ST(D1)=D1 and ST(D2)=D2 are given. (This condition means the sufficiency of T for D1 and D2.) Sufficiency implies a particular decomposition of the density matrices. This decomposition allows to deduce the exact condition for equality in the strong subadditivity of the von Neumann entropy.
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