monogamy of entanglement

Monogamy of entanglement is the rule that a quantum system can be strongly entangled with only one partner at a time. If two qubits are maximally entangled with each other, neither can share any entanglement with a third party; the entanglement is, so to speak, faithful. Spread your entanglement among several partners and the share with each must shrink, so that no one of them can be perfectly entangled with you.

This is unlike classical correlation, which can be freely shared. Three friends can all agree to vote the same way, each perfectly correlated with both of the others, and there is no limit to how widely such agreement spreads. Strong quantum entanglement refuses this generosity: there is a strict trade-off, captured by precise mathematical inequalities, that limits how much entanglement one party can hold with two or more others combined.

Monogamy is not just an elegant constraint; it is the quiet guardian of quantum security. In quantum key distribution, the fact that an eavesdropper cannot secretly become strongly entangled with the legitimate parties is exactly what keeps a shared key private. The same principle shows up across physics, from the structure of many-body ground states to debates about black-hole information, wherever the question is how a system can divide its entanglement among many neighbours at once.