The geometric measure of entanglement is a means to quantify the entanglement in a multi-partite system.
For a system consisting of
The geometric measure of entanglement in
with respect to all the separable states
with
This approach works for distinguishable particles or the spin systems. For identical or indistinguishable fermions or bosons, the full Hilbert space is not the tensor product of those of each individual particle. Therefore, a simple modification is necessary. For example, for identical fermions, since the full wave function