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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.

In a local gapped ground state, correlations and the entanglement that lower local interaction energies are concentrated within a finite correlation length. A degree of freedom deep inside a region uses most of its entanglement with nearby degrees of freedom that are also inside. Entanglement monogamy limits its simultaneous entanglement with the exterior, so only degrees of freedom within a correlation-length layer of the boundary can contribute extensively across the cut. Their number scales as the boundary area, suggesting the entanglement area lawThis is a physical argument rather than a proof from monogamy alone; locality and suitable ground-state assumptions are essential.

Entanglement monogamy says that strong entanglement between $A$ and $B$ limits the entanglement of either with an independent $C$. For qubits, the Coffman--Kundu--Wootters inequality isIn quantum cryptography, nearly maximal correlations between legitimate partners imply that an eavesdropper cannot hold a purification with equally strong correlations. Measuring an error rate therefore bounds the eavesdropper's information and permits privacy amplification.

In a local gapped ground state, correlations and the entanglement needed to lower a local interaction energy are concentrated over a finite distance. Degrees of freedom deep inside a region use most of their entanglement with nearby degrees of freedom that are also inside; entanglement monogamy limits their simultaneous entanglement with the exterior. Only degrees of freedom within a correlation length of the boundary can contribute extensively across the cut, giving an entanglement area lawMonogamy supplies the physical mechanism, while locality and suitable ground-state assumptions are essential; monogamy alone is not a general mathematical proof of an area law.