### Sewing states of quantum field theory. (arXiv:1911.11153v1 [hep-th])

Consider an $n$-partite system and denote by $\omega^{(i)}$ the local density matrix at site $A_i$. We say a pure $n$-partite state $|\Omega\rangle$ sews $\omega^{(i)}$ together if it reduces to $\omega^{(i)}$ on $A_i$ for all $i$. In finite quantum systems, density matrices can be sewn together only if their eigenvalues satisfy polygon inequalities. We show that…