Koen Thas

The geometry of generalized Pauli operators of N-qudit Hilbert space, and an application to MUBs

We prove that the set of non-identity generalized Pauli operators on the Hilbert space of N d-level quantum systems, d an odd prime, naturally forms a symplectic polar space of rank N and order d. This generalizes the solution (by the author) of a recent conjecture posed by Saniga-Planat (which covers the case d=2). As an application, we give a new short proof for the existence of maximal sets of MUBs (mutually unbiased bases) in Hilbert spaces of prime power dimension (also including the prime case).

Finite projective planes, Fermat curves, and Gaussian periods

One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences involving Fermat curves and Gaussian periods. In particular, we show that a non-Desarguesian flag-transitive projective plane of order

A Theorem Concerning Nets Arising from Generalized Quadrangles with a Regular Point

n

TRANSLATION GENERALIZED QUADRANGLES FOR WHICH THE TRANSLATION DUAL ARISES FROM A FLOCK

exists if and only if

Finite flag-transitive projective planes: a survey and some remarks

n>8

Generalized Quadrangles with an Abelian Singer Group

, the number

On symmetries and translation generalized quadrangles.

p=n^2+n+1

Solution of a question of Knarr

is prime, and the square of the absolute value of the Gaussian period

The Weyl functor. Introduction to Absolute Arithmetic

\,\sum_{a\in\D_n}\z^a\,

Unextendible Mutually Unbiased Bases (after Mandayam, Bandyopadhyay, Grassl and Wootters)

(