Abstract:
The
Mutually Unbiased Bases problem is to determine the maximal
number N(d) of orthonormal bases in a d-dimensional Hilbert
space, which are mutually unbiased in the following sense:
the inner product of any vectors from two different bases
have the same absolute value (namely d^(-1/2)). It is know
that N(d) cannot be greater than d+1 and this upper bound
can be reached when d is a power of a prime. We give a simplified
algebra proof of this fact with the help of Weil Sums. We
also propose a new combinatorial method to build mutually
unbiased bases in non-prime-power dimensions.
Biography:
Xiaohui
Bei was born in Liaoning. He received primary and secondary
school education in his hometown. Then he went to Tsinghua
University to pursue a BS degree in the department of Computer
Science and Technology. He is expected to graduate in 2008
and after that, he will become a PhD student in the theoretical
computer science group advised by Prof. Andrew Yao.
Xiaohui's
interest is in theoretical computer science, especially
in algorithm and complexity. He participated the ACM-ICPC
International Collegiate Programming Contest Beijing Site,
and won the second place in 2004 and first place in 2005.