Entanglement Breaking Rank and the existence of SIC POVMs

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 $d$.

arXiv commentUpdated version, Changes in the title and expositions

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Cited by in corpus (6)

• Discrete Wigner Functions from Informationally Complete Quantum Measurements
• Born's rule as a quantum extension of Bayesian coherence
• Lüders Channels and the Existence of Symmetric Informationally Complete Measurements
• $C^{\ast }$-extreme points of entanglement breaking maps
• Entanglement Breaking Channels, Stochastic Matrices, and Primitivity
• An extension of Bravyi-Smolin's construction for UMEBs