Comment on ‘Product states and Schmidt rank of mutually unbiased bases in dimension six’

Abstract A lemma by Chen et al (2017 J. Phys. A: Math. Theor. 50 475304 ) provides a necessary condition on the structure of any complex Hadamard matrix in a set of four mutually unbiased bases in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The proof of the lemma is shown to contain a mistake, ultimately invalidating three theorems derived in later publications.