Spins extracted from fermionic states and their entanglement properties

We investigate the spin states obtained by extracting $n$ electrons from closed-shell fermionic states. A partition of the system is defined through the introduction of the extraction modes. We derive the expression of the $n$-body reduced density matrices, which represent the extracted spin states. We show that these states exhibit different forms of spin entanglement, whose detection is discussed in terms of the spin squeezing inequalities.