Parametrization of spin-1 classical states

Olivier Giraud 1, Petr Braun 2, 3, Daniel Braun 4

Physical Review A 85 (2012) 032101

We give an explicit parametrization of the set of mixed quantum states and of the set of mixed classical states for a spin--1. Classical states are defined as states with a positive Glauber-Sudarshan P-function. They are at the same time the separable symmetric states of two qubits. We explore the geometry of this set, and show that its boundary consists of a two-parameter family of ellipsoids. The boundary does not contain any facets, but includes straight-lines corresponding to mixtures of pure classical states.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Institute of Physics, Saint-Petersburg University,
    Saint-Petersburg University
  • 3. Fachbereich Physik, Universitaet Duisburg-Essen,
    Universitaet Duisburg-Essen
  • 4. Laboratoire de Physique Théorique - IRSAMC (LPT),
    CNRS : UMR5152 – Université Paul Sabatier - Toulouse III