  We propose a Partial Lorentz Transformation (PLT) test for detecting
entanglement in a two qubit system. One can expand the density matrix of a two
qubit system in terms of a tensor product of $(\mathbb{I}, \vec{\sigma})$. The
matrix $A$ of the coefficients that appears in such an expansion can be
"squared" to form a $4\times4$ matrix $B$. It can be shown that the eigenvalues
$\lambda_0, \lambda_1, \lambda_2, \lambda_3$ of $B$ are positive. With the
choice of $\lambda_0$ as the dominant eigenvalue, the separable states satisfy
$\sqrt{\lambda_1}+\sqrt{\lambda_2}+\sqrt{\lambda_3}\leq \sqrt{\lambda_0}$.
Violation of this inequality is a test of entanglement. Thus, this condition is
both necessary and sufficient and serves as an alternative to the celebrated
Positive Partial Transpose (PPT) test for entanglement detection. We illustrate
this test by considering some explicit examples.
