Bell state
The four maximally entangled states of two qubits — quantum mechanics' simplest demonstration that the whole cannot be decomposed into parts.
In the state usually written |Φ+⟩, neither qubit is zero or one, yet both are guaranteed to agree when measured. Measure one and you instantly know the other's value, at any distance. Each qubit on its own, however, looks entirely random.
John Bell showed in 1964 that such correlations are stronger than any hidden-variable theory permits. Experiments since the 1970s have confirmed this repeatedly, and the 2022 Nobel Prize in Physics went to Aspect, Clauser and Zeilinger for exactly this work.