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We consider questions posed in a recent paper of Mandayam, Bandyopadhyay,Grassl and Wootters [10] on the nature of "unextendible mutually unbiasedbases." We describe a conceptual framework to study these questions, using aconnection proved by the author in [19] between the set of nonidentitygeneralized Pauli operators on the Hilbert space of $N$ $d$-level quantumsystems, $d$ a prime, and the geometry of non-degenerate alternating bilinearforms of rank $N$ over finite fields $\mathbb{F}_d$. We then supply alternativeand short proofs of results obtained in [10], as well as new general bounds forthe problems considered in loc. cit. In this setting, we also solve Conjecture1 of [10], and speculate on variations of this conjecture.

Unextendible mutually unbiased bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)