Introduces k-nets over algebras as a common framework for k-nets and MUBs, derives a rigidity property implying limited extensions for partial MUB sets when k ≤ √d, and shows certain group-based constructions cannot be completed.
The limitati ons of nice mutually unbiased bases
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Rigidity and a common framework for mutually unbiased bases and k-nets
Introduces k-nets over algebras as a common framework for k-nets and MUBs, derives a rigidity property implying limited extensions for partial MUB sets when k ≤ √d, and shows certain group-based constructions cannot be completed.