Entanglement of Indistinguishable Particles and its Quantification

We introduce geometric measures of entanglement for indistinguishable particles, which apply to mixed states, multipartite systems, and arbitrary dimensions. They are based on generalized (i.e., not necessarily finite) norms on the set of quantum states and lead to the first necessary and sufficient computational separability criterion in this general setting. The coherent approach developed in the paper allows us to compare, in particular, entanglement for fermionic and distinguishable particles: The entanglement measure for fermionic particles coincides with the corresponding entanglement measure for distinguishable particles up to a factor of $k!$ where $k$ is the number of particles involved. By this result the amount of entanglement emerging from fermi statistics alone is clearly separated from the overall amount of entanglement. Finally, our techniques are applied to entanglement related to Schmidt and Slater numbers.