Here is a nice thing you can do at a high school level--- show if it is possible to take a photograph in complete darkness.
Suppose you have a dark room, and you don't want to disturb it, you don't want to shine light on it. But you want to see what's in the room. You have access to a light source, a window into the room (or you are in the room), beam-splitters, and interferometers, but you want to ensure that at any time the probability of a photon getting detected inside the room is negligible. Can you take a picture?
Classically you can't do it, you either shine a photon into the room, or you don't. But, with a modification of the Elitzur-Vaidman bomb tester, you should be able to easily build a theoretical device which can scan a photograph of the room without ever allowing an appreciable probability of a photon ever being detected inside the room, outside your apparatus.
The mechanism has not been worked out in full, this is an old original idea of mine, but it is simple given the Elitzur Vaidman result. A sketch is as follows--- you do the Elitzur Vaidman thing, split a photon into N components with magnitude $\epsilon$, where $N\epsilon^2$ is small, and scatter all these little photon components off the room in separated bunches. You then have a rotating lens which collects the photon amplitude fraction that come back out the window, and interferes with the major component of the beam. You can detect interference when $N\epsilon$ is non-negligible, but this still makes it that a person inside the room will detect no photons. You can make the illumination going into the room arbitraily small, while allowing the interference effects to be detectable, and to reveal at which angles the photon returns to you, or if it is absorbed.
I do not know if this can be used to make a practical dark camera, but it is possible in principle, and it would make a nice high-school project which I think would be guaranteed a top prize, even if it is purely theoretical. It's another counterintuitive property of quantum mechanics, the counterfactual measurement.