Let's suppose we have two entangled particles that can either have the values of 1 or 0 when measured. Before measurement, both particles are in a superposition of both 1 and 0 and have a 50/50 chance of being 1 or 0. When one particle is then measured, then the other particle will have the opposite measurement of the first. So if one is 0 then the other will measure 1. But after measurement, if we now stop measuring both particles, can they both go back to the superposition state of being 0 or 1 and still remain entangled?

• A measurement brings the pair to an eigenstate of whatever measurement you made. From there, the state evolves according to the Schrodinger equation. If the Hamiltonian is "unentangled" (i.e. of the form $H\otimes J$ where $H$ and $J$ act on the state spaces for the individual particles), then it can never bring an unentangled state back to an entangled one. (Past history is of course irrelevant.) – WillO Dec 6 '18 at 19:08
• I think there is a really nice variant of this question for a research context, phrasing it in terms of weak measurements and the resulting decoherence... but probably the answer is still "no"? – CR Drost Dec 6 '18 at 21:33