On SIC-POVMs and MUBs in Dimension 6
Markus Grassl (IAKS, Universitaet Karlsruhe)
TL;DR
This paper explores the construction of MUBs and SIC-POVMs in dimension six, providing algebraic descriptions and establishing maximality of certain MUB sets, advancing understanding in non-prime-power dimensions.
Contribution
It offers an algebraic framework for SIC-POVMs in dimension six and proves the maximality of specific MUB sets, addressing a key challenge in non-prime-power dimensions.
Findings
Algebraic description of SIC-POVM in dimension six
Identification of maximal sets of three MUBs in dimension six
Progress towards constructing MUBs and SIC-POVMs in non-prime-power dimensions
Abstract
We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic description of a SIC-POVM in dimension six is given. Furthermore it is shown that several sets of three mutually unbiased bases in dimension six are maximal, i.e., cannot be extended.
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Taxonomy
TopicsCoding theory and cryptography · Algebraic structures and combinatorial models · graph theory and CDMA systems