Finite Geometries and Mutually Unbiased Bases

T. Olupitan, Chao Lei, Apostol Vourdas

Roger Howe

Andreas Klappenecker, Martin Rötteler

Joanne L. Hall, Jan Šťovíček

Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs.

Koen Thas

Joanne L. Hall, Jan Šťovíček

Mutually unbiased bases (MUBs) have been used in several cryptographic and communications applications. There has been much speculation regarding connections between MUBs and finite geometries. Most of which has focused on a connection with projective and affine planes. We propose a connection with higher dimensional projective geometries and projective Hjelmslev geometries. We show that this proposed geometric structure is present in several constructions of MUBs.