Because of the antisymmetry of their wave function, fermions always have a non-trivial entanglement. Intuitively, Slater determinants should be the least entangled states, and we investigate whether their reduced density matrices indeed minimize entanglement measures such as mutual information, entanglement of formation and squashed entanglement. To do this, we prove a quantitative version of subadditivity of entropy.

We are led to consider the Yang pairing state, which is a different fermionic state with a special extremal property: it has the largest eigenvalue any 2-particle reduced density matrix of a fermionic state can have. We reformulate an old conjecture by Yang regarding generalizations to k-particle reduced density matrices with k>2.

Insight into what mechanisms cause these extremal properties, and how we can prove them, requires a better understanding of the role played by antisymmetry and has connections with N-representability/the quantum marginal problem.

Coauthors: Eric A. Carlen, Rutgers University; Elliott H. Lieb, Princeton University