  Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are
constructed by using the algebra of Dirac $\gamma$ matrices in the space-time
of arbitrary dimension $d$, where the first kind can detect some BSD
relativistic and non-relativistic $m$-partite multispinor bound entangled
states in Hilbert space of dimension $2^{m\lfloor d/2\rfloor}$, including the
bipartite Bell-type and iso-concurrence type states in the four-dimensional
space-time ($d=4$). 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.Ud
