Greenberger-Horne-Zeilinger and W entanglement witnesses for the noninteracting Fermi gas

Journal Article · Mon Mar 15 04:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.032302· OSTI ID:21413286

Habibian, Hessam ^[1]; Clark, John W ^[2]; Behbood, Naeimeh ^[1]; Hingerl, Kurt ^[1]

---

1. Christian Doppler Labor fuer Oberflaechenoptische Methoden, Johannes Kepler Universitaet, Linz A-4040 (Austria)
2. Institut fuer Theoretische Physik, Johannes Kepler Universitaet, Linz A-4040 (Austria)

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/B and GHZ/W (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/B from GHZ/B 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/W 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/B genuine tripartite entanglement: three-party entanglement without any separable or biseparable admixture does not occur.

• OSTI ID: 21413286
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 81; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANGULAR MOMENTUM
BOUNDARY CONDITIONS
CALCULATION METHODS
DENSITY MATRIX
FERMI GAS
FERMIONS
FREQUENCY RANGE
GHZ RANGE
LINEAR PROGRAMMING
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATRICES
MIXED STATE
PARTICLE PROPERTIES
PERIODICITY
PROJECTION OPERATORS
QUANTUM ENTANGLEMENT
SPIN
THREE-BODY PROBLEM
VARIATIONS