H. Habibian, J.W. Clark, Naeimeh Behbood, Kurt Hingerl,
"Greenberger-Horne-Zeilinger and W entanglement witnesses for the noninteracting Fermi gas"
, in Physical review A: Atomic, Molecular, and Optical Physics, Vol. 81, Nummer 3, AMER PHYSICAL SOC, 2010, ISSN: 2469-9934
Original Titel:
Greenberger-Horne-Zeilinger and W entanglement witnesses for the noninteracting Fermi gas
Sprache des Titels:
Englisch
Original Kurzfassung:
The existence and nature of tripartite entanglement of a noninteracting
Fermi gas (NIFG) is investigated. Three classes of parametrized
entanglement witnesses (EWs) are introduced with the aim of detecting
genuine tripartite entanglement in the three-body reduced density
matrix and discriminating between the presence of the two types of
genuine tripartite entanglement, W\textbackslashB and
GHZ\textbackslashW (the convex set of B states is comprised of mixed
states of product and biseparable states; that of W states is comprised
of mixed states of B states and W-type pure entangled states; and the
GHZ (Greenberger-Horne-Zeilinger) set contains generic mixtures of any
kind for a tripartite system). By choosing appropriate EW operators,
the problem of finding GHZ and W EWs is reduced to linear programming.
Specifically, we devise W EWs based on a spin-chain model with periodic
boundary conditions, and we construct a class of parametrized GHZ EWs
by linearly combining projection operators corresponding to all the
different state-vector types arising for a three-fermion system. A
third class of EWs is provided by a GHZ stabilizer operator capable of
distinguishing W\textbackslashB from GHZ\textbackslashB
entanglement, which is not possible with W EWs. Implementing these
classes of EWs, it is found that all states containing genuine
tripartite entanglement are of W type, and hence states containing
GHZ\textbackslashW genuine tripartite entanglement do not arise. Some
genuine tripartite entangled states that have a positive partial
transpose (PPT) with respect to some bipartition are detected. Finally,
it is demonstrated that a NIFG does not exhibit ``pure''
W\textbackslashB genuine tripartite entanglement: three-party
entanglement without any separable or biseparable admixture does not
occur.
Sprache der Kurzfassung:
Englisch
Journal:
Physical review A: Atomic, Molecular, and Optical Physics
Forschungs-