[KSV02](Chapter 11 and 12)was one of the earliest introductions to channel distance by diamond norm. Reference [KSV02]A.Yu.Kitaev,A.H.Shen,M.N.Vyalyi,Classical and Quantum Computation, American Mathematical Society,2002. [NC0O]Michael Nielsen and Isaac Chuang,Quantum Computation and Quantum Information, Cambridge University Press,2000 [Wat1 1]John Watrous,Lecture notes for Theory of Ouantum Information,Fall 2011. [Will3]Mark M.Wilde,Quantum Information Theory,Cambridge University Press,2013[KSV02] (Chapter 11 and 12) was one of the earliest introductions to channel distance by diamond norm. Reference [KSV02] A. Yu. Kitaev, A. H. Shen , M. N. Vyalyi, Classical and Quantum Computation, American Mathematical Society, 2002. [NC00] Michael Nielsen and Isaac Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000. [Wat11] John Watrous, Lecture notes for Theory of Quantum Information, Fall 2011. [Wil13] Mark M. Wilde, Quantum Information Theory, Cambridge University Press, 2013