3 research outputs found
Matched witness for multipartite entanglement
We transform the way of finding entanglement criterion into two steps: to
obtain necessary criterion of separability by maximizing an algebra function
for a set of characteristic variables of the witness operator and the given
number of partitions, then to obtain the sufficient criterion by minimizing an
algebra function with respect to the characteristic variables for a given
quantum state. Our method avoids the semi-definite program calculation in the
witness operator entanglement detection. The necessary and sufficient criterion
of separability for the three qubit X shaped state is given to illustrate the
procedure of finding the criterion. We give the necessary and sufficient
criteria of the three partite and full separabilities for the four qubit noisy
GHZ state and the four qubit noisy cluster state.Comment: 8 pages, no figure
A hierarchy of entanglement criteria for four qubit symmetric Greenberger-Horne-Zeilinger diagonal states
With a two step optimization method of entanglement witness, we analytically
propose a set of necessary and sufficient entanglement criteria for four qubit
symmetric Greenberger-Horne-Zeilinger (GHZ) diagonal states. The criterion set
contains four criteria. Two of them are linear with density matrix elements.
The other two criteria are nonlinear with density matrix elements. The
criterion set has a nest structure. A proper subset of the criteria is
necessary and sufficient for the entanglement of a proper subset of the states.
We illustrate the nest structure of criterion set with the general Werner state
set and its superset the highly symmetric GHZ diagonal state set, they are
subsets of the symmetric GHZ diagonal state set.Comment: 10 pages, 3 figure
Precise detection of multipartite entanglement in four-qubit Greenberger--Horne--Zeilinger diagonal states
We propose a method of constructing the separability criteria for
multipartite quantum states on the basis of entanglement witnesses. The
entanglement witnesses are obtained by finding the maximal expectation values
of Hermitian operators and then optimizing over all possible Hermitian
operators. We derive a set of tripartite separability criteria for the
four-qubit Greenberger--Horne--Zeilinger (GHZ) diagonal states. The derived
criterion set contains four criteria that are necessary and sufficient for the
tripartite separability of the highly symmetric four-qubit GHZ diagonal states;
the criteria completely account for the numerically obtained boundaries of the
tripartite separable state set. One of the criteria is just the tripartite
separability criterion of the four-qubit generalized Werner states.Comment: 12 pages, 3 figures, almost published versio