A universal set of qubit quantum channels

Daniel Braun 1 Olivier Giraud 2 Ion Nechita 1 Clement Pellegrini 3 Marko Znidaric 4

Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2014, 47 (13), pp.135302. <10.1088/1751-8113/47/13/135302>

We investigate the set of quantum channels acting on a single qubit. We provide a compact generalization of the Fujiwara-Algoet conditions for complete positivity to non-unital qubit channels, which we then use to characterize the possible geometric forms of the pure output of the channel. We provide universal sets of quantum channels for all unital qubit channels as well as for all extremal (not necessarily unital) qubit channels, in the sense that all qubit channels in these sets can be obtained by concatenation of channels in the corresponding universal set. We also show that our universal sets are essentially minimal.

  • 1. Information et Chaos Quantiques (LPT)
  • 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 3. IMT - Institut de Mathématiques de Toulouse
  • 4. Department of Physics, Faculty of Mathematics and Physics