Greenberger-Horne-Zeilinger and W entanglement witnesses for the noninteracting Fermi gas
- Christian Doppler Labor fuer Oberflaechenoptische Methoden, Johannes Kepler Universitaet, Linz A-4040 (Austria)
- 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, Vol. 81, Issue 3; Other Information: DOI: 10.1103/PhysRevA.81.032302; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
DENSITY MATRIX
FERMI GAS
FERMIONS
GHZ RANGE
LINEAR PROGRAMMING
MIXED STATE
PERIODICITY
PROJECTION OPERATORS
QUANTUM ENTANGLEMENT
SPIN
THREE-BODY PROBLEM
ANGULAR MOMENTUM
CALCULATION METHODS
FREQUENCY RANGE
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATRICES
PARTICLE PROPERTIES
VARIATIONS