Bonn-Aachen International Center
for Information Technology





city life
cosec >students >Teaching >Summer 2006 

Progress on the mutually unbiased bases (MUBs) problem and application to quantum cryptography

Meera Sitharam ( University of Florida at Gainesville )

Thursday 22 June 2006, 15.00 sharp (s.t.), b-it 2.1 (seminar room)


The mutually unbiased bases (MUBs) problem is to find the maximum number of d dimensional orthonormal bases over the complex numbers such that every pair of bases is ``mutually unbiased:'' any pair of vectors chosen from different bases is as far apart as possible, that is, the 2 vectors have inner product modulus exactly 1/sqrt(d). Except for prime power dimensions d, no good bounds are known for the maximum number of MUBs in d dimensions. For example, the maximum number is not known even for d = 6 and it is not known if this number tends to infinity with d.
I will first motivate the problem by describing how MUBs can be used to encrypt quantum states. Following this, I will briefly survey what is known about the maximum number of MUBs in d dimensions: MUBs being natural and intuitive structures, the problem can be approached using a wide variety of mathematical tools and appears to be close to well known open problems. If time permits, I will sketch our recent result (joint with Boykin, Tiep, Wocjan) showing that the MUB problem is equivalent to a previously studied problem in finite group theory: orthogonal decomposition of certain Lie algebras.

Imprint, webmaster & more