ar X iv : q ua nt - p h / 04 09 18 4 v 1 2 7 Se p 20 04 Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes ?

ar X iv : q ua nt - p h / 04 09 18 4 v 2 2 5 N ov 2 00 4 Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes ?

This note is a short conceptual elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space as an analogue of an arc in a (finite) projective plane of order d. Complete sets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. In the Desarguesian case, the existence of two pri...

ar X iv : q ua nt - p h / 97 09 04 2 v 1 18 S ep 1 99 7 Measurement and state preparation via ion trap quantum computing

We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'Helon and G. The performance of a measurement shows some interesting patterns which are closely related to searching.

ar X iv : q ua nt - p h / 04 11 17 2 v 1 2 3 N ov 2 00 4 Information and Entropy in Quantum Theory

ar X iv : m at h - ph / 0 50 60 57 v 1 2 2 Ju n 20 05 Hjelmslev Geometry of Mutually Unbiased Bases

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space Hq, q = p r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration of points lying on a proper conic in a projective Hjelmslev plane defined over a Galois ring of characteristic p and rank r. The q vectors of a basis of Hq co...

ar X iv : q ua nt - p h / 02 03 04 6 v 1 1 1 M ar 2 00 2 Quantum imaging

We provide a brief overview of the newly born field of quantum imaging, and discuss some concepts that lie at the root of this field.