Lüders Channels and the Existence of Symmetric Informationally Complete Measurements

Abstract

The Lüders rule provides a way to define a quantum channel given a quantum measurement. Using this construction, we establish an if-and-only-if condition for the existence of a $d$-dimensional Symmetric Informationally Complete quantum measurement (a SIC) in terms of a particular depolarizing channel. Moreover, the channel in question satisfies two entropic optimality criteria.

9 pages. v2: Title and other changes to match journal version. Important postscript pointing to arXiv:1805.04583 by Pandey et al. Added proof of special case of conjecture appearing in v1