Source: http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

A delayed choice quantum eraser, first performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and Marlan O. Scully,[1] is an elaboration on a quantum eraser experiment involving the concepts considered in Wheeler's delayed choice experiment. It was designed to investigate peculiar consequences of the well-known double slit experiment in quantum mechanics, as well as the consequences of quantum entanglement.

In a quantum eraser experiment, one arranges to detect which one of the slits the photon passes through, but also to construct the experiment in such a way that this information can be "erased" after the fact.

In practice, this "erasure" of path information frequently means removing the constraints that kept photons following two different paths separated from each other.

In one experiment, rather than splitting one photon or its probability wave between two slits, the photon is subjected to a beam splitter. If one thinks in terms of a stream of photons being randomly directed by such a beam splitter to go down two paths that are kept from interaction, it is clear that no photon can then interfere with any other or with itself.

If the rate of photon production is reduced so that only one photon is entering the apparatus at any one time, however, it becomes impossible to understand the photon as only moving through one path because when their outputs are redirected so that they coincide on a common detector then interference phenomena appear.

This result is similar to that of the double-slit experiment, since interference is observed when it is not known which slit the photon went through, while no interference is observed when the path is known.

However, what makes this experiment possibly astonishing is that, unlike in the classic double-slit experiment, the choice of whether to preserve or erase the which-path information of the idler need not be made until after the position of the signal photon has already been measured by D0.

There is never any which-path information determined directly for the photons that are detected at D0, yet detection of which-path information by D3 or D4 means that no interference pattern is observed in the corresponding subset of signal photons at D0.

The results from Kim, et al.[1] have shown that whether the idler photon is detected at a detector that preserves its which-path information (D3 or D4) or a detector that erases its which-path information (D1 or D2) determines whether interference is seen at D0, even though the idler photon is not observed until after the signal photon arrives at D0 due to the shorter optical path for the latter.

Some have interpreted this result to mean that the delayed choice to observe or not observe the path of the idler photon will change the outcome of an event in the past. However, an interference pattern may only be observed after the idlers have been detected (i.e., at D1 or D2).