A Note on the Extreme Points of Positive Quantum Operations

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Abstract

In this paper, an error in the proof of Theorem 4.9 in Gudder's paper (Int. J. Theor. Phys. 47(1):268–279, 2008) is pointed out and it is proved that if ε ≈ {E1, E2, …, En} ∈ 𝒬pos(ℋ)\𝒬pro(ℋ) such that Ei ∈ ℂI\{0} and Ej ∉ ℂI for some i,j in {1,2, …, n}, then ε ∉ Ext[𝒬pos(ℋ)].

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