This is a supplement to the Web page "Elements of Finite Geometry." The list of selected papers below is intended only as a starting point; it is by no means complete. The order is, roughly, chronological.

Harmonic Analysis on a Galois Field and Its Subfields, by A. Vourdas, J Fourier Anal Appl (2008) 14: 102–123 Quantum
systems
with positions and momenta on a Galois field, by A.
Vourdas, Journal of Physics: Conference Series 104 (2008) 012014 Quantum designs - foundations of a non-commutative theory of
designs Picturing qubits in phase space, by William K. Wootters (pdf, arXiv Aug. 2003, 26 pp.) MUBs,
polytopes, and finite geometries, by Ingemar Bengtsson (pdf, arXiv
July 2004, 15 pp.) Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem, by Juan Pablo Paz, Augusto Jose Roncaglia, and Marcos Saraceno (pdf, arXiv Nov 2004, 18 pp.) Mutually
Unbiased
Bases
and
Covers of Complete Bipartite Graphs, by Chris
Godsil and Aidan Roy (pdf, 61 slides, Nov. 19, 2004) The limitations of nice mutually unbiased bases, by Michael Aschbacher, Andrew M. Childs, and Pawel Wocjan (pdf, arXiv Dec. 2004, 7 pp.) Viewing
sets
of
mutually
unbiased bases as arcs in finite projective planes,
by Metod Saniga and Michel Planat (pdf, 4 pp., March 29, 2005) Quantum Kaleidoscopes and Bell's Theorem, by P.K. Aravind (Int. J. Mod. Phys. B20, 1711-1729, 2006), quant-ph/0508130, submitted 17 Aug. 2005 (pdf, 20 pp.) Quantum
Designs:
MUBs,
SICPOVMs,
and (a little bit) More, by Markus Grassl
(pdf, May 2006, 28 pp.)
A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements, by Michel Planat, Haret C. Rosu, and Serge Perrine (pdf, Oct. 12, 2006, 20 pp.) Multiple Qubits as
Symplectic Polar Spaces of Order Two, by Metod Saniga,
arXiv:quant-ph/0612179, submitted 21 Dec. 2006 Geometry
of Two-Qubits, by Metod Saniga (pdf, Jan. 25, 2007, 17 pp.) Related material: An
Intensive
Mini-Workshop on Finite Projective Geometries in Quantum Theory,
Abstracts (August 1 – 4,
2007, Tatranská Lomnica / Slovakia) (from website of Metod Saniga) The Geometry of Qubits, by Steven H. Cullinane (html, Aug. 12, 2007) |