Dresden 2011 – wissenschaftliches Programm
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Q: Fachverband Quantenoptik und Photonik
Q 61: Quantum Information: Concepts and Methods 4
Q 61.4: Vortrag
Freitag, 18. März 2011, 11:15–11:30, SCH A118
A Simple Construction of Cyclic Mutually Unbiased Bases — •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
Many applications of complete sets of mutually unbiased bases (MUBs)
in the field of quantum information theory are known. In particular,
in the context of quantum cryptography they yield generalizations of the
six-state protocol for qubits. Recently it was
shown that in even prime-power dimensions such MUBs can be generated
by a single unitary operator [1,2] so that they are ’cyclic’.
In this contribution we present a method for constructing
cyclic MUBs in higher dimensions recursively.
This method enables one to construct
generators of complete sets of cyclic MUBs for very high dimensions
without elaborate numerical calculation.
These results may be relevant for high-dimensional
generalizations of the quantum cryptographic six-state protocol as well
as possible applications in quantum state discrimination.
H. F. Chau, IEEE Trans. Inf. Theory 49, 457 (2003)
R. Gow, arXiv:math/0703333v2 (2007)