Entangled systems cannot be described by assigning an independent state to each part. Their measurement outcomes are correlated more strongly than any classical model allows.
Learning objectives
Distinguish classical correlation from entanglement.
Summarise what Bell tests demonstrate.
Explain why entanglement does not transmit information on its own.
Joint states
For two qubits there are four basis states. Some joint states factor into one state per qubit; entangled states do not. The whole carries information that no individual part contains.
Bell inequalities
Bell tests compare observed correlations against the maximum achievable by local models with pre-set values. Experiments repeatedly exceed that classical bound, which rules out broad classes of local explanations.
No faster-than-light signalling
Local measurement statistics on one half of an entangled pair are unchanged by what happens to the other half. Correlations appear only when both result sets are compared through a classical channel.