Is quantum entanglement invariant in special relativity?

Quantum entanglements are of fundamental importance in quantum physics ranging from the quantum information processing to the physics of black hole. Here, we show that the quantum entanglement is not invariant in special relativity. This suggests that nearly all aspects of quantum information processing would be affected significantly when relativistic effects are considered because present schemes are based on the general assumption that entanglement is invariant. There should be additional protocols to compensate the variances of entanglement in in quantum information processing. Furthermore, extending our results to general relativity may provide clues to the fate of the information contained in an entangled Hawking pair inside and outside the event horizon as black hole evaporates.