The purpose of this paper is to generalize fermionic coherent states for two-level systems described by pseudo-Hermitian Hamiltonian [1], to n-level systems. Central to this task is the expression of the coherent states in terms of generalized Grassmann variables.These kind of Grassmann coherent states satisfy bi-overcompleteness condition instead of over-completeness one, as it is reasonably expected because of the biorthonormality of the system. Choosing an appropriate Grassmann weight function resolution of identity is examined. Moreover Grassmannian coherent and squeezed states of deformed group SU q (2) for three level pseudo-Hermitian system are presented.
One of the problems concerning entanglement witnesses (EWs) is the construction of them by a given set of operators. Here several multi-qubit EWs called stabilizer EWs are constructed by using the stabilizer operators of some given multi-qubit states such as GHZ, cluster and exceptional states. The general approach to manipulate the multi-qubit stabilizer EWs by exact(approximate) linear programming (LP) method is described and it is shown that the Clifford group play a crucial role in finding the hyper-planes encircling the feasible region. The optimality, decomposability and non-decomposability of constructed stabilizer EWs are discussed.
A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension d 1 ⊗ d 2 ⊗ ... ⊗ d n . The novelty of this work comes from the fact that the feasible regions turn out to be convex polygons, hence the manipulation of these EWs reduces to linear programming which can be solved exactly by using simplex method. The decomposability and non-decomposability of these EWs are studied and it is shown that it has a close connection with eigenvalues and optimality of EWs. Also using the Jamio lkowski isomorphism, the corresponding possible positive maps, including the generalized reduction maps of Ref. [21], are obtained.
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