An operational link between MUBs and SICs
Roberto Beneduci, Tom Bullock, Paul Busch, Claudio Carmeli, Teiko, Heinosaari, Alessandro Toigo
TL;DR
This paper establishes a direct operational connection between mutually unbiased bases and symmetric informationally complete POVMs in prime power dimensions, but shows such a link does not exist in dimension 6.
Contribution
It demonstrates a strong link between MUBs and SICs in prime power dimensions assuming SICs exist, and proves the absence of such a link in dimension 6.
Findings
Strong link between MUBs and SICs in prime power dimensions
No such link exists in dimension 6
Assumption of SIC existence is crucial for the link
Abstract
We exhibit an operational connection between mutually unbiased bases and symmetric infomationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures in all prime power dimensions. We also demonstrate that a similar link cannot exists in dimension 6.
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