Quantum Entanglement Monogamy

Entanglement is monogamous: if particle A is maximally entangled with B, it cannot be entangled with C at all. This fundamental constraint (Coffman-Kundu-Wootters 2000) is the reason quantum key distribution is secure — any eavesdropper stealing entanglement reveals themselves.

E(A:B) Entanglement 0.70

E(A:C) Entanglement 0.20

n Qubits (chain) 4

E(A:B)

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E(A:C)

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CKW Residual τ

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Monogamy Satisfied?

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Max E(A:C) allowed

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CKW Inequality (Coffman-Kundu-Wootters):
C²(A|B) + C²(A|C) ≤ C²(A|BC)
C = concurrence. Residual τ = C²(A|BC) − C²(A|B) − C²(A|C) ≥ 0 is "three-party entanglement"