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Paper IPM / Physic / 7283  


Abstract:  
It is shown that for a given bipartite density matrix and by
choosing a suitable separable set (instead of a product set) on
the separable?entangled boundary, the optimal Lewenstein?Sanpera
(LS) decomposition (with respect to an arbitrary separable set)
can be obtained via a direct optimization procedure for a generic
entangled density matrix. On the basis of this, we obtain the
optimal LS decomposition for some bipartite systems such as 2⊗2 and 2 ⊗3 Bell decomposable (BD) states,
a generic two qubit state in Wootters basis, isoconcurrence
decomposable states, states obtained from BD states via
oneparameter and threeparameter local operations and classical
communications (LOCC), d ⊗d Werner and isotropic
states and a oneparameter 3 ⊗3 state. We also obtain
the optimal decomposition for multipartite isotropic states. It
is shown that in all 2 ⊗2 systems considered here the
average concurrence of the decomposition is equal to the
concurrence. We also show that for some 2 ⊗3 Bell
decomposable states, the average concurrence of the decomposition
is equal to the lower bound of the concurrence of the state
presented recently in Lozinski et al (2003 Preprint
quantph/0302144), so an exact expression for concurrence of these
states is obtained. It is also shown that for a d ⊗d
isotropic state where decomposition leads to a separable and an
entangled pure state, the average Iconcurrence of the
decomposition is equal to the Iconcurrence of the state.
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