We find that the m-separability and k-partite entanglement of a multipartite quantum system is correlated with quantum coherence of the same with respect to complete orthonormal bases, distinguishable under local operations and classical communication in certain partitions. In particular, we show that the geometric measure of m-inseparable entanglement of a multipartite quantum state is equal to the square of minimum fidelity-based quantum coherence of the state with respect to complete orthonormal bases, that are locally distinguishable in a partition into m-parties.
We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for
N spin-
21 fermions distributed over
2L modes (single-particle states). The measure is defined on the
2L qubit space isomorphic to the Fock space for
2L single-particle states. This entanglement measure is defined for a given partition of
2L modes containing $m\ensuremath{\geqslant}2$ subsets. Thus this measure applies to $m\ensuremath{\leqslant}2L$ partite fermionic systems where
L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitary operators corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems.