Entanglement monogamy

Entanglement monogamy limits how strongly one subsystem can be entangled with several independent partners.

For a pure state of three qubits, the squared concurrence obeys $C_{A:BC}^2\ge C_{AB}^2+C_{AC}^2$. In particular, if $A$ and $B$ form a maximally entangled pair, then $A$ has no entanglement with $C$.

An entanglement area law bounds the entropy of a region by a constant times the size of its boundary.

If a bipartition cuts $n_{\partial }$ tensor-network bonds of dimension at most $\chi$, its Schmidt rank is at most ${\chi }^{n_{\partial }}$ and its entanglement entropy is at most $n_{\partial }\log \chi$.