Belltests

Bell tests are experiments designed to test Bell inequalities, which place constraints on statistical correlations predicted by local hidden-variable theories. Such theories assume that measurement outcomes are determined by pre-existing properties and that signals cannot travel faster than light. Quantum mechanics, by contrast, predicts correlations that can violate these bounds when particle pairs are entangled.

In a typical Bell test, a source emits pairs of entangled particles and sends them to two distant observers who choose measurement settings independently and randomly. Each observer records results, usually dichotomic like plus or minus. After many trials, the data are used to compute a Bell parameter, such as the CHSH statistic S = E(a,b) + E(a,b′) + E(a′,b) − E(a′,b′), where E is the correlation function for measurement settings a, a′, b, b′. Local realism requires |S| ≤ 2, while quantum mechanics permits up to |S| = 2√2.

Bell tests have a long history from Bell’s 1964 theorem to the classical experiments of Aspect in the 1980s. In 2015, several experiments achieved loophole-free Bell tests, addressing both the locality and detection loopholes. Nonetheless, practical tests continue to refine closing additional loopholes and exploring high-efficiency photon detectors and fast randomization.

Beyond foundational interest, Bell tests underpin device-independent quantum information protocols, offering security guarantees based solely on observed nonlocal correlations. They have been implemented across platforms, including photonic, ionic, and solid-state qubits, and remain central to studies of quantum nonlocality and quantum information science.