Introduction to finite fields and their applications
Introduction to finite fields and their applications
New construction of mutually unbiased bases in square dimensions
Quantum Information & Computation
Beyond stabilizer codes .I. Nice error bases
IEEE Transactions on Information Theory
Semi-regular relative difference sets with large forbidden subgroups
Journal of Combinatorial Theory Series A
On the equivalence between real mutually unbiased bases and a certain class of association schemes
European Journal of Combinatorics
Mutually unbiased bases and orthogonal decompositions of Lie algebras
Quantum Information & Computation
Efficient 2-designs from bases exist
Quantum Information & Computation
Constructions of approximately mutually unbiased bases
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
| Hi-index | 0.00 |
Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets.