Geodesic
On the geometry of two qubits
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 69-73.

Voir la notice de l'article provenant de la source Math-Net.Ru

Two qubits are considered as a spinor in the four-dimensional complex Hilbert space that describes the state of a four-level quantum system. This system is basic for quantum computation and is described by the generalized Pauli equation including the generalized Pauli matrices. The generalized Pauli matrices constitute the finite Pauli group $\mathcal P_2$ for two qubits of order $2^6$ and nilpotency class $2$. It is proved that the commutation relation for the Pauli group $\mathcal P_2$ and the incidence relation in an Hadamard $2$-$(15,7,3)$ design give rise to equivalent incidence matrices. 
@article{FPM_2012_17_5_a3,
     author = {T. E. Krenkel},
     title = {On the geometry of two qubits},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {69--73},
     publisher = {mathdoc},
     volume = {17},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a3/}
}
TY  - JOUR
AU  - T. E. Krenkel
TI  - On the geometry of two qubits
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2012
SP  - 69
EP  - 73
VL  - 17
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a3/
LA  - ru
ID  - FPM_2012_17_5_a3
ER  - 
%0 Journal Article
%A T. E. Krenkel
%T On the geometry of two qubits
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2012
%P 69-73
%V 17
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a3/
%G ru
%F FPM_2012_17_5_a3
T. E. Krenkel. On the geometry of two qubits. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 5, pp. 69-73. http://geodesic.mathdoc.fr/item/FPM_2012_17_5_a3/

[1] Dembowski P., Wagner A., “Some characterizations of finite projective spaces”, Arch. Math., 11 (1960), 465–459 | DOI | MR

[2] Havlicek H., Odehnal B., Saniga M., “Factor group generated polar spaces and (multi-)qudits”, SIGMA, 5 (2009), 096 | DOI | MR | Zbl

[3] Payne S. E., Thas J. A., Finite Generalized Quadrangles, Pitman, Boston, 1984 | MR | Zbl

[4] Planat M., Saniga M., “On the Pauli graphs of $N$-qudits”, Quantum Inform. Comput., 8:1–2 (2008), 127–146 | MR | Zbl

[5] Thas K., “The geometry of generalized Pauli operators of $N$-qudit Hilbert space, and applications to MUBs”, Europhysics Letters, 86:6 (2009), 60005 | DOI