  A fundamental resource in any communication and computation task is the
amount of information that can be transmitted and processed. Information
encoded in a classical system is limited by the dimension d_c of the system,
i.e., the number of distinguishable states. A system with d_c=2^n classical
states can carry n bits of classical information. Information encoded in a
quantum system is limited by the dimension d_q of the Hilbert space of the
system, i.e., the number of perfectly distinguishable quantum states. A system
with d_q=2^n perfectly distinguishable quantum states can carry n qubits of
quantum information. Physical systems of higher dimensions may enable more
efficient and powerful information processing protocols. The dimension is
fundamental in quantum cryptography and random number generation, where the
security of many schemes crucially relies on the system's dimension. From a
fundamental perspective, the dimension can be used to quantify the
non-classicality of correlations, since classical simulation of correlations
produced by a quantum system of dimension d_q may require a classical system of
dimension d_c >> d_q. For all these reasons, a fundamental problem in
information theory is to assess the (classical or quantum) dimension of a
physical system in a "device-independent" scenario, i.e., without referring to
the system's specifications, which may be under control of a dishonest
supplier, eavesdropper or saboteur. In this contribution we report experiments
realizing this goal for systems emitted by a black box. Our results indicate
that dimension witnesses utilized in the experiments may become a powerful tool
for testing systems provided by unreliable sources.
