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Mutually Unbiased Bases and Their Symmetries

Institut für Angewandte Physik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
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Quantum Reports 2019, 1(2), 226-235; https://doi.org/10.3390/quantum1020020
Received: 30 September 2019 / Revised: 2 November 2019 / Accepted: 6 November 2019 / Published: 8 November 2019
We present and generalize the basic ideas underlying recent work aimed at the construction of mutually unbiased bases in finite dimensional Hilbert spaces with the help of group and graph theoretical concepts. In this approach finite groups are used to construct maximal sets of mutually unbiased bases. Thus the prime number restrictions of previous approaches are circumvented and this construction principle sheds new light onto the intricate relation between mutually unbiased bases and characteristic geometrical structures of Hilbert spaces.
Keywords: mutually unbiased bases; group representations; graphs; quantum information mutually unbiased bases; group representations; graphs; quantum information
MDPI and ACS Style

Alber, G.; Charnes, C. Mutually Unbiased Bases and Their Symmetries. Quantum Reports 2019, 1, 226-235.

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