 Entanglement monogamy

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.