Device-independent tests of classical and quantum dimensions

Phys Rev Lett. 2010 Dec 3;105(23):230501. doi: 10.1103/PhysRevLett.105.230501. Epub 2010 Nov 30.


We address the problem of testing the dimensionality of classical and quantum systems in a "black-box" scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalize the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.