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Article Dans Une Revue Revista Mexicana de Fisica Année : 2011

About the Dedekind psi function in Pauli graphs

Résumé

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.
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Dates et versions

hal-00543978 , version 1 (07-12-2010)

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Michel Planat. About the Dedekind psi function in Pauli graphs. Revista Mexicana de Fisica, 2011, S57 (3), pp.107-112. ⟨hal-00543978⟩
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