Quantum Physics related to Finite Geometry

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
(In German: Quantendesigns - Grundzüge einer nichtkommutativen Designtheorie), by Gerhard Zauner (dissertation, 1999, ps.gz, 74 pp.)

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:

On the Pauli Graphs of N-Qudits
, by Michel Planat and Metod Saniga (pdf, June 11, 2007, 17 pp.)

The Veldkamp Space of Two-Qubits
, by Metod Saniga, Michel Planat, Petr Pracna, and Hans Havlicek, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA 3 (2007), 075) (pdf, June 18, 2007, 7 pp.), and the following cited papers:
Pauli Operators of N-Qubit Hilbert Spaces and the Saniga–Planat Conjecture, by K. Thas, Chaos Solitons Fractals, to appear (as of June 18, 2007)
The Geometry of Generalized Pauli Operators of N-Qudit Hilbert Space, by K. Thas, Quantum Information and Computation, submitted (as of June 18, 2007)

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)