Monogamy of Entanglement

Entanglement cannot be freely shared: if two qubits are maximally entangled, neither can be entangled with any third party.

Entanglement is not promiscuous

Monogamy of entanglement is the principle that quantum entanglement cannot be arbitrarily shared among many parties. Unlike classical correlation, which one system can share freely with any number of others, entanglement is a limited resource distributed under a strict trade-off.

The extreme case

If qubit A is maximally entangled with qubit B — say they form a Bell state — then A cannot be entangled at all with any qubit C. The Bell pair uses up all of A's entanglement capacity. C sees A as completely uncorrelated. Maximal entanglement is exclusive.

The quantitative bound

For three qubits, the Coffman-Kundu-Wootters inequality formalises this: the entanglement A shares with B, plus the entanglement A shares with C, cannot exceed the total entanglement between A and everything else. There is a fixed budget, and dividing it among partners means giving each one less.

Contrast with classical correlation

Classical correlations are monogamy-free. A random bit can be perfectly copied and correlated with a million others simultaneously. That entanglement resists this is one of the sharpest distinctions between quantum and classical information, and it is rooted in the no-cloning theorem.

Why it matters

Monogamy underwrites the security of quantum key distribution: if two legitimate parties share strong entanglement, an eavesdropper is provably locked out of correlating with their key. It also constrains the structure of many-body entangled states and appears in analyses of black-hole information. In computing it shapes how entanglement can be routed and distributed across a processor.