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Q: Fachverband Quantenoptik und Photonik
Q 23: Poster 2: Intersectional Session
Q 23.6: Poster
Dienstag, 15. März 2011, 18:00–21:00, P1
Cyclic Mutually Unbiased Bases and the Fibonacci Sequence — •Ulrich Seyfarth1, Kedar Ranade2, and Gernot Alber1 — 1Institut für Angewandte Physik, Technische Universität Darmstadt, 64289 Darmstadt, Germany — 2Institut für Quantenphysik, Universität Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany
The construction of mutually unbiased bases (MUBs) is of high interest in
quantum information science.
MUBs are called cyclic if they can
be constructed by repeated applications of a single unitary operator.
To get a deeper notion of how to contruct
complete sets of cyclic MUBs in arbitrary dimensions it is important to explore
their mathematical structure.
Based on recent work [1] a connection between
cyclic MUBs and the Fibonacci sequence is established.
This connection enables one
to find complete sets of cyclic MUBs in arbitrary even prime-power
dimensions. Thereby, known properties of the Fibonacci sequence yield a
simplified construction method conveying a better notion of complete sets
of cyclic MUBs.
O. Kern, K. S. Ranade and U. Seyfarth, J. Phys. A, 43, 275305 (2010)