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 D_1 and D_2 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(D_1)=D_1 and ST(D_2)=D_2 are given. (This condition means the sufficiency of T for D_1 and D_2.) 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.

13 pages, LATEX

References in corpus (3)

• Reversing quantum dynamics with near-optimal quantum and classical fidelity
• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• Monotonicity of quantum relative entropy revisited

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