Structure of Sufficient Quantum Coarse-Grainings

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• 作者：Mil¨¢n Mosonyi and D¨¦nes Petz
• 关键词：coarse ; graining ; quantum states ; sufficiency ; transpose mapping ; strong subadditivity of entropy
• 刊名：Letters in Mathematical Physics
• 出版年：2004
• 出版时间：2004
• 年：2004
• 卷：68
• 期：1
• 页码：19-30
• 全文大小：131 KB

文摘

Let H and be finite-dimensional Hilbert spaces, T: B(H) B() be a coarse-graining and D₁, D₂ be density matrices on H . In this Letter the consequences of the existence of a coarse-graining : B() B(H) satisfying T(D_s)=D_s are given. (This means that T is sufficient for D₁ and D₂.) It is shown that D_s= _p=1r _s(p) SH_sH (p)RH(p) (s=1,2) should hold with pairwise orthogonal summands and with commuting factors and with some probability distributions _s(p) for 1 p r (s=1,2). This decomposition allows to deduce the exact condition for equality in the strong subadditivity of the von Neumann entropy.