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Entanglement monogamy describes limits on sharing quantum entanglement among several partners. If two qubits form a pure Bell state, their joint state cannot also be correlated with a third system: the Bell pair already has a pure joint density operator, so the full state factorizes from the third system.

For partially entangled states, a quantitative sharing rule depends on the measure and subsystem dimensions. The Coffman--Kundu--Wootters inequality bounds the sum of squared pairwise concurrences for three qubits by the entanglement of one qubit with the other two together. Squaring and the chosen measure matter; one cannot assume an identical linear inequality for every entanglement measure. Classical correlations can be shared much more freely, distinguishing monogamy from a general ban on correlated triples.

Entanglement monogamy says that maximal entanglement with one independent system excludes entanglement with another. For three qubits this is quantified by the Coffman--Kundu--Wootters inequalityFor example, if $AB$ is a maximally entangled state, then $C_{AB}=1$ and the global state factorizes as $|{\psi }^{-}{⟩}_{AB}\otimes |\varphi {⟩}_C$ up to local unitaries, so $C_{AC}=C_{BC}=0$. The three-qubit GHZ state instead has entanglement across every one-versus-two cut but no pairwise concurrence after the third qubit is traced out.