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

Lower bound on entanglement in subspaces defined by Young diagrams