An application of positive definite functions to the problem of MUBs
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- by Mihail N. Kolountzakis, Máté Matolcsi and Mihály Weiner PDF
- Proc. Amer. Math. Soc. 146 (2018), 1143-1150 Request permission
Abstract:
We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most $d+1$ MUBs in $\mathbb {C}^d$, and it may also lead to a proof of non-existence of complete systems of MUBs in dimension 6 via a conjectured algebraic identity.References
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Additional Information
- Mihail N. Kolountzakis
- Affiliation: Department of Mathematics and Applied Mathematics, University of Crete, Voutes Campus, 700 13 Heraklion, Greece
- Email: kolount@gmail.com
- Máté Matolcsi
- Affiliation: Department of Analysis, Budapest University of Technology and Economics (BME), H-1111, Egry J. u. 1, Budapest, Hungary — and — Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H-1053, Realtanoda u 13-15, Budapest, Hungary
- Email: matomate@renyi.hu
- Mihály Weiner
- Affiliation: Department of Analysis, Budapest University of Technology and Economics (BME), H-1111, Egry J. u. 1, Budapest, Hungary
- Email: mweiner@renyi.hu
- Received by editor(s): January 5, 2017
- Received by editor(s) in revised form: April 16, 2017
- Published electronically: October 12, 2017
- Additional Notes: The first author was partially supported by grant No 4725 of the University of Crete
The second author was supported by the ERC-AdG 321104 and by NKFIH-OTKA Grant No. K104206
The third author was supported by the ERC-AdG 669240 QUEST “Quantum Algebraic Structures and Models” and by NKFIH-OTKA Grant No. K104206 - Communicated by: Alexander Iosevich
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 1143-1150
- MSC (2010): Primary 43A35; Secondary 15A30, 05B10
- DOI: https://doi.org/10.1090/proc/13829
- MathSciNet review: 3750226