Yakir Aharonov and colleagues have proposed a rather provocative experiment which has been dubbed the quantum Cheshire cat. The Physics World review of this paper has a rather interesting description of this proposal.
In the latest work, Aharonov has teamed up with Sandu Popescu of the University of Bristol, Daniel Rohrlich of Ben Gurion University and Paul Skrzypczyk, then at Cambridge University. The group has devised an experiment, which it says can be implemented with current technology, in which individual horizontally polarized photons pass through a beamsplitter and then traverse a series of optical devices before being registered in one of three detectors. When leaving the beamsplitter, each photon is in some kind of superposition of two different paths that it can take to reach the other devices, the two paths representing the two arms of an interferometer.
The devices are chosen and arranged so that the first of the detectors only clicks when the photon is in a specific superposition state, and it is this state that is post-selected. The researchers then consider what happens to the photon – the Cheshire cat – and its polarization – the grin – in that post-selected state. They find that while any photon detector would reveal the photon to always travel along the left-hand arm, a polarization detector would occasionally measure angular momentum in the right-hand one. "We seem to see what Alice saw," the researchers write, "a grin without a cat!"
The researchers point out that this analysis falls down because it relies on the two kinds of detector being used at different times, and that if they were to be used simultaneously, the detectors would always show the photon and its polarization together in the same arm. But Aharonov and colleagues argue that they can "regain the paradox" by carrying out what are known as "weak measurements", which do not provide definitive values of particle parameters but do have the virtue of not completely destroying a particle's quantum state, as usually happens during the measurement process.
You can read the entire review, or the actual paper, from the links given above. Note that there are experts who still have questions about what is being measured in this scheme.