Monogamy of entanglement

Content sourced from Wikipedia, licensed under CC BY-SA 3.0.

Monogamy of entanglement is a fundamental limit in quantum physics: entanglement, the spooky connection between particles, cannot be freely shared with many partners. If two qubits A and B are maximally entangled, they cannot be entangled with a third qubit C at all. Even if A and B are not perfectly entangled, their connection still limits how much either one can be entangled with C.

For systems with three or more qubits, this restriction is captured by the CKW inequality. In simple terms, the more strongly A is entangled with B, the less it can be entangled with other qubits. The exact math only quantifies this trade-off, but the idea is clear: entanglement is a finite resource that can’t be spread without limit.

Monogamy is a purely quantum phenomenon and has no classical counterpart. Classically, you can copy information and create many copies that share the same relationship with another variable. In the quantum world, entangled states cannot be copied this way, so the entanglement you have with one partner restricts what you can share with others.

Why it matters: monogamy underpins the security of quantum cryptography. If two parties share strong entanglement, an eavesdropper cannot be equally entangled with them, helping detect tampering. It also influences theoretical ideas in areas like black hole physics.

History in brief: the three-qubit case was proven in 2000 by Coffman, Kundu, and Wootters. The multipartite extension followed in 2006 by Osborne and Verstraete. A simple way to see the idea is to consider A and B in a perfect Bell (maximally entangled) state; in any larger system including C, C cannot be entangled with A or B, so the AB link stays intact while C remains separate.