# Can quantum disentanglement be triggered by time dilation?

The question is really one question that leads to the final one:

1. Is it possible to realize a qubit that naturally flips between two quantum states on a definite and fixed period without any ongoing external stimulation?

2. If so, if such a qubit were forced into entanglement with another such oscillating qubit and then one of the qubits accelerated up to very near light-speed, would relativistic time dilation lead to disentanglement/desynchronization of these two "qubit clocks"?

• why was this question downvoted? – Oke Uwechue Aug 27 at 15:11

(1) Yes. A simple example is when the two states are not eigenstates of the energy operator. Imagine that the two lowest energy eigenstates are $$|1\rangle$$ and $$|2\rangle$$, with energy $$E_1$$ and $$E_2$$ respectively, and form a superposition state from them.
A good example are the two lowest energy states of a 1D double well, where $$|1\rangle$$ would be the lowest energy symmetric and $$|2\rangle$$ the anti-symmetric state. The states $$|+\rangle=(|1\rangle+|2\rangle)/\sqrt{2}$$ and $$|-\rangle=(|1\rangle-|2\rangle)/\sqrt{2}$$ would then correspond to having the system in the left or right well respectively. But if placed in state $$|+\rangle$$ at $$t=0$$ the state will evolve as $$(|1\rangle e^{-iE_1t/\hbar}+|2\rangle e^{-iE_2t/\hbar})/\sqrt{2}$$, wobbling back and forth between the two wells at a frequency set by the difference in energy between the two states.