Multipartite entanglement in fermionic systems via a geometric measure

Abstract

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 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 >= 2 subsets. Thus this measure applies to m <= 2L partite fermionic system 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 unitaries corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems. To the best of our knowledge, there is no usable entanglement measure of m > 3 partite fermionic systems in the literature, so that this is the first measure of multipartite entanglement for fermionic systems going beyond the bipartite and tripartite cases.

25 pages, 8 figures

References in corpus (11)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Localizable Entanglement
• Entanglement in fermionic systems
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Three fermions with six single particle states can be entangled in two inequivalent ways
• An Experimentally accessible geometric measure for entanglement in $N$-qubit pure states
• Particle partitioning entanglement in itinerant many-particle systems
• Analytic Expressions for Geometric Measure of Three Qubit States
• Duality and the geometric measure of entanglement of general multiqubit W states
• Genuine tripartite entanglement in the non-interacting Fermi gas

Cited by in corpus (4)

• Entanglement in indistinguishable particle systems
• A measure of tripartite entanglement in bosonic and fermionic systems
• Segre maps and entanglement for multipartite systems of indistinguishable particles
• Entanglement of formation for qubit-qudit system using partition of qudit sytem into a set of qubit system