Lower bound on entanglement in subspaces defined by Young diagrams

Abstract

Eigenvalues of 1-particle reduced density matrices of $N$-fermion states are upper bounded by $1/N$, resulting in a lower bound on entanglement entropy. We generalize these bounds to all other subspaces defined by Young diagrams in the Schur-Weyl decomposition of ${\otimes }^N{\mathbb{C}}^d$.

Published version, 21 pages