Separability and entanglement of two qubits density matrices using Lorentz transformations
Abstract
Explicit separability of general two qubits density matrices is related to Lorentz transformations. We use the 4-dimensional form Rμ,ν(μ,ν=0,1,2,3) of the Hilbert–Schmidt (HS) decomposition of the density matrix. For the generic case, in which Lorentz transformations diagonalize Rμ,ν into s0,s1,s2,s3, we give relations between the sμ and the Rμ,ν. 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 β=1 which is not reachable physically.
