Philip Ball writes in Nature mag:
Causation has been a key issue in quantum mechanics since the mid-1930s, when Einstein challenged the apparent randomness that Niels Bohr and Werner Heisenberg had installed at the heart of the theory. Bohr and Heisenberg's Copenhagen interpretation insisted that the outcome of a quantum measurement — such as checking the orientation of a photon's plane of polarization — is determined at random, and only in the instant that the measurement is made. No reason can be adduced to explain that particular outcome. But in 1935, Einstein and his young colleagues Boris Podolsky and Nathan Rosen (now collectively denoted EPR) described a thought experiment that pushed Bohr's interpretation to a seemingly impossible conclusion. ...This research is somewhat interesting, but it is not what it appears.
Brukner's group in Vienna, Chiribella's team and others have been pioneering efforts to explore this ambiguous causality in quantum mechanics3, 4. They have devised ways to create related events A and B such that no one can say whether A preceded and led to (in a sense 'caused') B, or vice versa. ...
The trick they use involves creating a special type of quantum 'superposition'. ... The two observable states can be used as the binary states (1 and 0) of quantum bits, or qubits, which are the basic elements of quantum computers.
The researchers extend this concept by creating a causal superposition. In this case, the two states represent sequences of events: a particle goes first through gate A and then through gate B (so that A's output state determines B's input), or vice versa.
They find an ambiguity in the path of the photon, but there are always such ambiguities in quantum mechanics. In a simple double-slit experiment, where a light source sends photons thru a slit A and slit B to a screen, the detector on the screen cannot tell you whether the photo went thru slit A or B. The preferred interpretation is that the light is some sort of quantum wave that goes thru both slits. The light is not really photons until they hit the detectors.
This experiment does not really violate causality as the term is usually understood. It is just another of many experiments that are hard to interpret if you think of light as Newtonian particles. Such experiments convinced physicists that light is a wave about 200 years ago. A century ago light was found to be a funny quantized wave, but not a particle in the way you normally think of particles.
I don't agree with calling light a particle, but I also don't agree with saying that it is random up until the instant of a measurement. We don't really know how to make sense out of such statements. Quantum mechanics is a theory about making predictions about observations, and I think Bohr and Heisenberg would say that it doesn't make any sense to talk about the path of the photon (such as going thru slit A or B, or going from A to B or B to A) unless you are actually measuring it.