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Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)

Department of Mathematics, Ghent University, Ghent 9000, Belgium
Academic Editor: Jay Lawrence
Entropy 2016, 18(11), 395; https://doi.org/10.3390/e18110395
Received: 7 September 2016 / Revised: 25 October 2016 / Accepted: 31 October 2016 / Published: 11 November 2016
(This article belongs to the Section Quantum Information)
We consider questions posed in a recent paper of Mandayam et al. (2014) on the nature of “unextendible mutually unbiased bases.” We describe a conceptual framework to study these questions, using a connection proved by the author in Thas (2009) between the set of nonidentity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d a prime, and the geometry of non-degenerate alternating bilinear forms of rank N over finite fields F d . We then supply alternative and short proofs of results obtained in Mandayam et al. (2014), as well as new general bounds for the problems considered in loc. cit. In this setting, we also solve Conjecture 1 of Mandayam et al. (2014) and speculate on variations of this conjecture. View Full-Text
Keywords: mutually unbiased bases; Pauli operator; symplectic polar space mutually unbiased bases; Pauli operator; symplectic polar space
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Thas, K. Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters). Entropy 2016, 18, 395.

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