Physics – Quantum Physics
Scientific paper
2010-12-07
Revista Mexicana de Fisica S57, 3 (2011) 107-112
Physics
Quantum Physics
Proceedings of Quantum Optics V, Cozumel to appear in Revista Mexicana de Fisica
Scientific paper
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.
No associations
LandOfFree
About the Dedekind psi function in Pauli graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with About the Dedekind psi function in Pauli graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and About the Dedekind psi function in Pauli graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-480300