The limitations of nice mutually unbiased bases
Journal of Algebraic Combinatorics: An International Journal
On the equivalence between real mutually unbiased bases and a certain class of association schemes
European Journal of Combinatorics
Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power
Cryptography and Communications
Exotic complex Hadamard matrices and their equivalence
Cryptography and Communications
Unbiased complex Hadamard matrices and bases
Cryptography and Communications
Limits on entropic uncertainty relations for 3 and more MUBs
Quantum Information & Computation
Mutually unbiased bases and orthogonal decompositions of Lie algebras
Quantum Information & Computation
Constructions of approximately mutually unbiased bases
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
The monomial representations of the Clifford group
Quantum Information & Computation
| Hi-index | 0.00 |
We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s2 provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (s, k)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bounds on the asymptotic growth of the number of mutually orthogonal Latin squares (based on number theoretic sieving techniques), we obtain that the number of mutually unbiased bases in dimensions d = s2 is greater than s1/14.8 for all s but finitely many exceptions. Furthermore, our construction gives more mutually orthogonal bases in many non-prime-power dimensions than the construction that reduces the problem to prime power dimensions.