Mainz 2026 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
Q: Fachverband Quantenoptik und Photonik
Q 67: Poster – Quantum Information
Q 67.29: Poster
Donnerstag, 5. März 2026, 17:00–19:00, Philo 2. OG
Statistical properties of quantum ensembles on hyperspheres — •Max Tartler and Reinhold Walser — Institut für Angewandte Physik, TU Darmstadt, Hochschulstraße 4A, 64289, Darmstadt
Quantum states are described by density operators and carry the entire information of a physical system. The Bloch sphere provides a geometric representation of all possible quantum states for spin 1/2-systems [1]. The question arises how quantum systems of higher dimension, such as multipartite ones, can be understood geometrically.
In this contribution, we give a geometric representation of quantum states in arbitrary dimensions. The key to this approach is the Cholesky decomposition of positive definite matrices [2]. One finds that the entire Hilbert space of N dimensions can be mapped onto a sector of the real unit hypersphere in N2 dimensions. We analyze where special classes of quantum states are located in this picture. Furthermore, the statistical properties of homogeneously distributed quantum states on the hypersphere are resolved through the computation of the probability distribution function of the density matrices.
[1] Quantum Computation and Quantum Information: 10th Anniversary Edition, Michael A. Nielsen, Isaac L. Chuang p. 105 (2010)
[2] Matrix Analysis, Roger A. Horn, Charles R. Johnson p. 441 (2013)
Keywords: Density operator; Cholesky decomposition; Hypersphere; Statistics