Multi-line geometry of qubit-qutrit and higher-order pauli operators

International Journal of Theoretical Physics

Volumn 47, Issue 4, 2008, Pages 1127-1135

  Planat, Michel ^a   Baboin, Anne Céline ^a   Saniga, Metod ^b  

^a CNRS   (France)

^b ASTRONOMICAL INSTITUTE   (Slovakia)

Author keywords

Finite projective geometries; Generalized Pauli operators; Pauli graphs

Indexed keywords

EID: 41549107985     PISSN: 00207748     EISSN: 15729575     Source Type: Journal    
DOI: 10.1007/s10773-007-9541-9     Document Type: Article

References (18)

1. Bandyopadhyay, S., Boykin, P.O., Roychowdhury, V., Vatan, F.: A new proof for the existence of mutually unbiased bases. Algorithmica 34, 512-528 (2002)
2. Planat, M., Rosu, H.C., Perrine, S.: A survey of finite algebraic geometrical structures underlying mutually unbiased measurements. Found. Phys. 36, 1662-1680 (2006)
3. Klimov, A.B., Sanchez-Soto, L.L., de Guise, H.: Multicomplementary operators via finite Fourier transform. J. Phys. A 38, 2747-2760 (2005)
4. Planat, M., Saniga, M., Kibler, M.: Quantum entanglement and projective ring geometry. SIGMA 2, Paper 066 (2006)
5. 3-x〉 and quantum entanglement: the Mermin "magic" square/pentagram. Theor. Math. Phys. 151, 625-631 (2007)
6. Saniga, M., Planat, M., Pracna, P.: Projective ring line encompassing two-qubits. Theor. Math. Phys. (2006, accepted). quant-ph/0611063
7. Planat, M., Saniga, M.: On the Pauli graphs of N-qubits. Quantum Int. Comput. 8, 127-146 (2008)
8. Payne, S.E., Thas, J.A.: Finite Generalized Quadrangles. Pitman, Boston (1984)
9. Saniga, M., Planat, M.: Multiple qubits and symplectic polar spaces of order two. Adv. Stud. Theor. Phys. 1, 1-4 (2007)
10. Thas, K.: Pauli operators of N-qubit Hilbert spaces and the Saniga-Planat conjecture. Chaos, Solitons Fractals (2007, to appear)
11. Planat, M., Saniga, M.: Pauli graph and finite projective lines/geometries. In: Opt. Optoelectron. SPIE Proceedings, vol. 6583 (2007)
12. Saniga, M., Planat, M., Kibler, M.R., Pracna, P.: A classification of the projective lines over small rings. Chaos, Solitons Fractals 33, 1095-1102 (2007)
13. Batten, L.M.: Combinatorics of Finite Geometries, 2nd edn. Cambridge University Press, Cambridge (1997)
14. Saniga, M., Planat, M., Pracna, P., Havlicek, H.: The Veldkamp space of two-qubits. SIGMA 3, Paper 075 (2007)
15. Grassl, M.: Quantum designs: MUBs, SICPOVMs, and (a little bit) more. Preprint available at avalon.ira.uka.de/home/grassl/paper/CEQIP_QDesigns.pdf
16. Mermin, N.D.: Hidden variables and two theorems of John Bell. Rev. Mod. Phys. 65, 803-815 (1993)
17. Blunck, A., Havlicek, H.: Projective representations I: Projective lines over a ring. Abh. Math. Semin. Univ. Hamb. 70, 287-299 (2000)
18. Havlicek, H.: Divisible designs, Laguerre geometry, and beyond. Quaderni del Seminario Matematico di Brescia 11, 1-63 (2006). A preprint available from http://www.geometrie.tuwien.ac.at/havlicek/dd-laguerre.pdf