Entanglement Breaking Rank and the existence of SIC POVMs


Abstract in English

We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the entanglement breaking rank of the channel $mathfrak Z: M_d to M_d$ defined by begin{align*} mathfrak Z(X) = frac{1}{d+1}(X+text{Tr}(X)mathbb I_d) end{align*} is $d^2$ if and only if there exists a symmetric informationally-complete POVM in dimension $d$.

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