Quantifying Quantumness and the Quest for Queens of Quantum

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

New Journal of Physics 12 (2010) 063005

We introduce a measure of  »quantumness » for any quantum state in a finite dimensional Hilbert space, based on the distance between the state and the convex set of classical states. The latter are defined as states that can be written as a convex sum of projectors onto coherent states. We derive general properties of this measure of non-classicality, and use it to identify for a given dimension of Hilbert space what are the ‘Queen of Quantum’ states, i.e. the most non-classical quantum states. In three dimensions we obtain the Queen of Quantum state analytically and show that it is unique up to rotations. In up to 11-dimensional Hilbert spaces, we find the Queen of Quantum states numerically, and show that in terms of their Majorana representation they are highly symmetric bodies, which for dimensions 5 and 7 correspond to Platonic bodies.

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