Relativistic entanglements of spin 1/2 particles with general momentum

In this paper, the Lorentz transformations of entangled Bell states with general momentum not necessarily orthogonal to the boost direction and spin are studied. We extend quantum correlations and Bell's inequality to the relativistic regime by considering normalized relativistic observables. It is shown that quantum information along the direction perpendicular to the boost is eventually lost, and Bell's inequality is not always violated for entangled states in special relativity. This could impose restrictions on certain quantum information processing, such as quantum cryptography using massive particles.