Is quantum entanglement affected by time dilation? Is quantum entanglement affected by time dilation?
Let's say one of the entangled pair is accelerated to very high speed. When both the entangled particles are observed at the same time, will they have the opposite spin?
 A: A relativistic boost entails a momentum-dependent Wigner rotation that changes the spin direction by an angle dependent on the qubit's momentum, see  https://arxiv.org/abs/quant-ph/0203051. If the qubit is not initially in a momentum eigenstate, which practically is always the case, the Wigner rotation will "entangle" its spin and momentum degrees of freedom. The result is that the qubit's spin state, obtained after averaging out the momentum part, will show an apparent "decoherence".
In this sense the answer to the question is negative: if one qubit of an entangled pair is boosted to some relativistic velocity, a simultaneous spin measurement in one reference frame, along the original spin polarization direction, may not produce the expected correlation or anti-correlation. 
The problem can be avoided either by adjusting the measured spin direction(s), or better, by redefining the "qubit spin" as a projection of the helicity along an eigendirection of the boost, see https://arxiv.org/abs/quant-ph/0312040. In any case, since a Wigner rotation amounts to a unitary transformation on the overall state space, a boost to another inertial frame, and with it the corresponding time dilation, does not affect overall spin-momentum entanglement. 
On the other hand, boosting to a non-inertial frame poses much more serious problems of potential entanglement loss through the Unruh effect.
