Lüders Channels and the Existence of Symmetric Informationally Complete Measurements
arXiv:1907.10999 · doi:10.1103/PhysRevA.100.062327
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 -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.
arXiv comment9 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
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