Testing the Hilbert space dimension
  Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describes such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and Quantum Information applications. 
Nicolas Brunner, Stefano Pironio, Antonio Acin, Nicolas Gisin, Andre   Allan Methot, and Valerio Scarani