Experimental Device-independent Tests of Classical and Quantum Dimensions
Abstract
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 dc of the system, i.e., the number of distinguishable states. A system with dc=2n classical states can carry n bits of classical information. Information encoded in a quantum system is limited by the dimension dq of the Hilbert space of the system, i.e., the number of perfectly distinguishable quantum states. A system with dq=2n 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 dq may require a classical system of dimension dc >> dq. 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.