Inspired by this article which uses a $|+\rangle$ state as a control for a $CSWAP$, I realised you can conditionally measure a qubit by (maybe) swapping it with an empty ancilla, measuring it and (maybe) swapping it back.
If measurement changes the top qubit then the second $H$ gate should put it back into the |+> state and we should measure random results. If the measurement doesn't change the top qubit, then it should turn the $|+\rangle$ back to $|0\rangle$, deterministically measuring 0. Right?
If so, then I'm hoping there's some extension of the uncertainty principle that would imply that because there is no knowledge about whether the second qubit was measured, we could learn something about the first qubit. I hope.
Of course I've tried to test this but I don't believe the qiskit simulator and none of the IBM devices allow operations to take place after measurement ("Qubit measurement not the final instruction. "). So can anyone think of a way I could test it? Does this count as a Bell Test? Has this been tried before? Am I missing something obvious?
Not sure if this is the right place to post this but just interested to hear people's thoughts/predictions.