Testing the Hilbert space dimension
arXiv:0802.0760 · doi:10.1103/PhysRevLett.100.210503
Abstract
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.
4 pages, 1 figure; Accepted for publication in PRL