On SIC-POVMs and MUBs in Dimension 6

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.

Results on maximal sets of MUBs in dimension 4 together with an appendix with the 48 vectors in dimension 6 are added. Omission in Lemma 2 corrected

References in corpus (3)

• Symmetric Informationally Complete Quantum Measurements
• A new proof for the existence of mutually unbiased bases
• Discrete phase space based on finite fields

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