Testing the Dimension of Hilbert Spaces
Nicolas Brunner, Stefano Pironio, Antonio Acín, Nicolas Gisin, André Allan Méthot, Valerio Scarani · Physical Review Letters · 2008
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 describe 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.