  Explicit separability of general two qubits density matrices is related to
Lorentz transformations. We use the 4-dimensional form R(u,v=0,1,2,3) of the
Hilbert-Schmidt (HS) decomposition of the density matrix. For the generic case
in which Lorentz transformations diagonalize R(u,v=0,1,2,3) (into
s(0),s(1),s(2),s(3)) we give relations between the R parameters and the s
parameters. In particular we consider two cases: a) Two qubits density matrices
with one pair of linear terms in the HS decomposition. b) Two qubits density
matrices with two or three symmetric pairs of linear terms. Some of the
theoretical results are demonstrated by numerical calculations. The four
non-generic cases (which may be reduced to case a) are analyzed and the
non-generic property is related explicitly to Lorentz velocity beta=1 which is
not reachable physically

Quantum Physics