91 research outputs found
2 and 3-dimensional Hamiltonians with Shape Invariance Symmetry
Via a special dimensional reduction, that is, Fourier transforming over one
of the coordinates of Casimir operator of su(2) Lie algebra and 4-oscillator
Hamiltonian, we have obtained 2 and 3 dimensional Hamiltonian with shape
invariance symmetry. Using this symmetry we have obtained their eigenspectrum.
In the mean time we show equivalence of shape invariance symmetry and Lie
algebraic symmetry of these Hamiltonians.Comment: 24 Page
Quantum Discord for Generalized Bloch Sphere States
In this study for particular states of bipartite quantum system in 2n?2m
dimensional Hilbert space state, similar to m or n-qubit density matrices
represented in Bloch sphere we call them generalized Bloch sphere states(GBSS),
we give an efficient optimization procedure so that analytic evaluation of
quantum discord can be performed. Using this optimization procedure, we find an
exact analytical formula for the optimum positive operator valued measure
(POVM) that maximize the measure of the classical correlation for these states.
The presented optimization procedure also is used to show that for any concave
entropy function the same POVMs are sufficient for quantum discord of mentioned
states. Furthermore, We show that such optimization procedure can be used to
calculate the geometric measure of quantum discord (GMQD) and then an explicit
formula for GMQD is given. Finally, a complete geometric view is presented for
quantum discord of GBSS. Keywords: Quantum Discord, Generalized Bloch Sphere
States, Dirac matrices, Bipartite Quantum System. PACs Index: 03.67.-a,
03.65.Ta, 03.65.UdComment: 26 pages. arXiv admin note: text overlap with arXiv:1107.5174 by
other author
Multi-qubit stabilizer and cluster entanglement witnesses
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.Comment: 57 pages, 2 figure
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