Four. 2016-2002 clearly equals 4…,or 14
I haven’t seen the PBS discussion, but Omphaloskeptic provided the right answer in this thread: you can’t use a quantum eraser to predict the future, because if all you have access to is the data gathered by your detector, you’ll never see an interference pattern—whether the idler is directed to the which path-information conserving or destroying set of detectors. In the first case, there simply won’t be an interference pattern; in the second, there’ll be a set of two patterns, phase-shifted such that the peaks of one exactly cancel out the troughs of the other—leading to exactly the same distribution of counts. It’s only if you then postselect on that data, picking out only those signals where the corresponding idler was detected at one of the which path-destroying detectors, that an interference pattern becomes visible.
Also, there’s no elaboration on the experiment that can do the trick—the quantum no-communication theorem shows that one can’t use quantum correlations to communicate information faster than light.