Lower bound on entanglement in subspaces defined by Young diagrams

TL;DR

This paper extends bounds on entanglement entropy for fermionic states to all subspaces defined by Young diagrams, broadening understanding of quantum entanglement in complex subspace structures.

Contribution

It generalizes eigenvalue bounds on reduced density matrices from fermionic states to all subspaces characterized by Young diagrams in the Schur-Weyl decomposition.

Findings

Eigenvalue bounds are extended to all Young diagram-defined subspaces.

Lower bounds on entanglement entropy are established for these subspaces.

The results deepen understanding of entanglement structure in quantum systems.

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 $\otimes^N\mathbb{C}^d$.