Maximal Orbital Entanglement from Non-Interacting Fermions

Abstract

Orbital rotations are used in quantum many-body physics and chemistry to reduce the complexity of quantum states by compressing their correlation into a small set of relevant orbitals. In striking contrast, quantum information processing strives for the opposite: orbitals that maximize entanglement as a resource. Motivated by this, we prove that Slater determinants of $N$ fermions on a lattice of $d_A + d_B = d$ sites, although free of particle correlation, can carry up to $\min\{d_A, d_B, N, d-N\}$ ebits of orbital entanglement. Given enough particles and holes, this equals the maximum over all fermionic states. For arbitrary free states, we derive the maximal orbital total correlation in closed form for all bipartitions, the finest partition, and all partitions of up to five sites, using new majorization relations for Hermitian matrices. Taken together, these results turn mean-field states, the starting point of most many-body methods in physics and chemistry, into a viable resource for quantum information processing.