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arXiv · 1805.04583

Entanglement Breaking Rank and the existence of SIC POVMs

Satish K. Pandey·Vern I. Paulsen·Jitendra Prakash·Mizanur Rahaman
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Abstract

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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Satish K. Pandey, Vern I. Paulsen, Jitendra Prakash, Mizanur Rahaman. 2020-07-31. Entanglement Breaking Rank and the existence of SIC POVMs. https://doi.org/10.1063/1.5045184

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