Testing the dimension of Hilbert spaces.
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.
Brunner
Nicolas
N
Group of Applied Physics, University of Geneva, Geneva, Switzerland.
Pironio
Stefano
S
Acin
Antonio
A
Gisin
Nicolas
N
Méthot
André Allan
AA
Scarani
Valerio
V