16 research outputs found
Robustness of Entanglement for Bell Decomposable States
We propose a simple geometrical approach for finding the robustness of
entanglement for Bell decomposable states of 2 otimes 2 quantum systems. It is
shown that the robustness of entanglement is equal to the concurrence. We also
present an analytical expression for two separable states that wipe out all
entanglement of these states. Finally the random robustness of these states is
also obtained.Comment: 11 pages, Late
Generalized Master Function Approach to Quasi-Exactly Solvable Models
By introducing the generalized master function of order up to four together
with corresponding weight function, we have obtained all quasi-exactly solvable
second order differential equations. It is shown that these differntial
equations have solutions of polynomial type with factorziation properties, that
is polynomial solutions Pm(E) can be factorized in terms of polynomial Pn(E)
for m not equal to n. All known quasi-exactly quantum solvable models can be
obtained from these differential equations, where roots of polynomial Pn(E) are
corresponding eigen-values.Comment: 21 Page
Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems
It is shown that for a given bipartite density matrix and by choosing a
suitable separable set (instead of product set) on the separable-entangled
boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via
optimization for a generic entangled density matrix. Based on this, We obtain
optimal L-S decomposition for some bipartite systems such as and
Bell decomposable states, generic two qubit state in Wootters
basis, iso-concurrence decomposable states, states obtained from BD states via
one parameter and three parameters local operations and classical
communications (LOCC), Werner and isotropic states, and a one
parameter state. We also obtain the optimal decomposition for
multi partite isotropic state. It is shown that in all systems
considered here the average concurrence of the decomposition is equal to the
concurrence. We also show that for some Bell decomposable states
the average concurrence of the decomposition is equal to the lower bound of the
concurrence of state presented recently in [Buchleitner et al,
quant-ph/0302144], so an exact expression for concurrence of these states is
obtained. It is also shown that for isotropic state where
decomposition leads to a separable and an entangled pure state, the average
I-concurrence of the decomposition is equal to the I-concurrence of the state.
Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition,
Concurrence, Bell decomposable states, LOCC}
PACS Index: 03.65.UdComment: 31 pages, Late
Bell-states diagonal entanglement witnesses for relativistic and non-relativistic multispinor systems in arbitrary dimensions
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are
constructed by using the algebra of Dirac matrices in the space-time
of arbitrary dimension , where the first kind can detect some BSD
relativistic and non-relativistic -partite multispinor bound entangled
states in Hilbert space of dimension , including the
bipartite Bell-type and iso-concurrence type states in the four-dimensional
space-time (). By using the connection between Hilbert-Schmidt measure and
the optimal EWs associated with states, it is shown that as far as the spin
quantum correlations is concerned, the amount of entanglement is not a
relativistic scalar and has no invariant meaning. The introduced EWs are
manipulated via the linear programming (LP) which can be solved exactly by
using simplex method. The decomposability or non-decomposability of these EWs
is investigated, where the region of non-decomposable EWs of the first kind is
partially determined and it is shown that, all of the EWs of the second kind
are decomposable. These EWs have the preference that in the bipartite systems,
they can determine the region of separable states, i.e., bipartite
non-detectable density matrices of the same type as the EWs of the first kind
are necessarily separable. Also, multispinor EWs with non-polygon feasible
regions are provided, where the problem is solved by approximate LP, and in
contrary to the exactly manipulatable EWs, both the first and second kind of
the optimal approximate EWs can detect some bound entangled states.
Keywords: Relativistic entanglement, Entanglement Witness, Multispinor,
Linear Programming, Feasible Region. PACs Index: 03.65.UdComment: 62 page