Abstract
We study the problem of detecting multipartite entanglement among indistinguishable fermionic particles. A multipartite concurrence for pure states of $N$ identical fermions, each one having a $d$-dimensional single-particle Hilbert space, is introduced. Such entanglement measure, in particular, is optimized for maximally entangled states of three identical fermions that play a role analogous to the usual (qubit) Greenberger-Horne-Zeilinger state. In addition, it is shown that the fermionic multipartite concurrence can be expressed as the mean value of an observable, provided two copies of the composite state are available.
Highlights
Entanglement is both a central key for understanding quantum phenomena and a useful resource for the implementation of quantum information tasks [1,2]
We explicitly show how the concurrence measure can be written in terms of the mean value of an observable given that a twofold copy of the state in question is available
A generalization of the entanglement criterion (14) that holds for arbitrary bipartitions M : N − M of the complete system is necessary in order to construct a multipartite concurrence measure, analogous to Eq (2), valid for identical fermions
Summary
Entanglement is both a central key for understanding quantum phenomena and a useful resource for the implementation of quantum information tasks [1,2]. Various bipartite entanglement measures for pure N -fermion states have been discussed, yet these measures are, in general (for N > 2), difficult to implement [5]. The available entanglement measures for bipartite systems become applicable, and adequate generalizations can account for real multipartite correlations [23,24]. We introduce the definition of separability in fermionic systems and present a concurrence measure for a pure state with N = 2.
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