This is a common misconception. (The Copenhagen interpretation of) QM is a local theory, in the sense that there's no faster-than-light travel of information.

Otherwise you'd have to take into account what's happening at the other end of the universe in order to successfully predict the outcome of experiments. (Which I hear is what the people working on Bohmian mechanics struggle with.)

It's been a while since I studied this, and I know that some Copenhagenist try to wiggle their way out of this, but if you consider the probability waves in the Copenhagen interpretation to be "real" and "measurement" to cause their collapse, book-keeping information by the universe would seem to have to travel at faster than the speed of light, IIRC.

On the other hand, it's certainly been proven that this cannot be used to transmit information that you might like to at faster than the speed of light. So causality is preserved in any case.

In the Everett interpretation, everything is local.