Theoriekolloquium
Dec. 10, 2015 at 4 p.m. in Newton-Raum, Staudinger Weg 9, 01-122Prof. Dr. P.G.J. van Dongen
Institut für Physik, KOMET 7
peter.vandongen@uni-mainz.de
Jun.-Prof. Dr. J. Marino
Institut für Physik, KOMET 7
jamarino@uni-mainz.de
In recent years, mutually unbiased bases for quantum systems have attracted interest among theoretical physicsts, mathematicians and experimental physicists. Two orthonormal bases are unbiased if the transition probabilities between any two of its states are equal. The eigenstates of two different spin components and the eigenstates of position and momentum of a quantum particle provide well-known examples. Mutual unbiasedness can be understood as a quantitative expression of complementarity which played an important role in the early development of quantum mechanics. I will summarize what is known about mutually unbiased bases and what makes them attractive. They are, for example, highly efficient to reconstruct unknown quantum states in terms of expectation values. However, it is not know whether the required sets of mutually bases always exist: already for a Hilbert space of dimension six it is not known how to construct them. The existence problem represents an unsolved mathematical problem, which is open for three decades. Some physicists suspect that the problem is related to a deep and unexpected link between quantum mechanics and number theory.