About the Dedekind psi function in Pauli graphs
| Autor: | Planat, Michel R. P. |
|---|---|
| Přispěvatelé: | Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174) (FEMTO-ST), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), Université de Technologie de Belfort-Montbeliard (UTBM)-Ecole Nationale Supérieure de Mécanique et des Microtechniques (ENSMM)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph]
Quantum Physics 03.67.Lx 02.10.Ox 02.20.-a 02.10.De 02.40.Dr [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph] Mathematics - Number Theory FOS: Mathematics FOS: Physical sciences Number Theory (math.NT) [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics Quantum Physics (quant-ph) [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] [SPI.MAT]Engineering Sciences [physics]/Materials |
| Zdroj: | Revista Mexicana de Física S Revista Mexicana de Física S, 2011, 57 (3), pp.107-112 Revista Mexicana de Fisica Revista Mexicana de Fisica, Sociedad Mexicana de Física, 2011, S57 (3), pp.107-112 |
| ISSN: | 0035-001X |
| Popis: | We study the commutation structure within the Pauli groups built on all decompositions of a given Hilbert space dimension $q$, containing a square, into its factors. The simplest illustrative examples are the quartit ($q=4$) and two-qubit ($q=2^2$) systems. It is shown how the sum of divisor function $\sigma(q)$ and the Dedekind psi function $\psi(q)=q \prod_{p|q} (1+1/p)$ enter into the theory for counting the number of maximal commuting sets of the qudit system. In the case of a multiple qudit system (with $q=p^m$ and $p$ a prime), the arithmetical functions $\sigma(p^{2n-1})$ and $\psi(p^{2n-1})$ count the cardinality of the symplectic polar space $W_{2n-1}(p)$ that endows the commutation structure and its punctured counterpart, respectively. Symmetry properties of the Pauli graphs attached to these structures are investigated in detail and several illustrative examples are provided. Comment: Proceedings of Quantum Optics V, Cozumel to appear in Revista Mexicana de Fisica |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|