The motivation for this comment came from a popular article " Quantum mischief rewrites the laws of cause and effect" (see this), which tells both about the theoretical work of Lucien Hardy (this) and related experimental work, in particular about the following experimental finding (this).
Photon beam goes through a spin splitter to form a superposition of photons going along two paths. At the first path they go through A and then through B having some effect on the photons. At second splitter the order of A and B is changed. After that the beams are superposed and it is found that the photons in a causally indefinite state in the sense that the effects of both AB and BA are superposed. In classical physics this is impossible.
The finding is claimed to demonstrate causal indefiniteness: one does not know whether A causes B or B causes A. Classically  that is in the framework provided by fixed causal order dictated by Minkowski space  this seems to be the case.
Is this interpretation correct? Is one really forced to give up causality in the standard form? The rules of standard quantum theory are consistent with the finding but should one change the views about the notion of spacetime?
 Lightcone of M^{4} characterizes the causal structure of Minkowski space in special relativity and is the basic notion of QFTs. In curved spacetime of GRT, the lightcone however depends on the metric of spacetime. Causal structure is dynamical. The intuitive view is that in quantum gravity causality becomes somehow fuzzy since there is no unique spacetime anymore. What this nonuniqueness means is not clear. For instance, could it correspond to what happens in the path integral over spacetimes?
 The problem is that one cannot compare the causal structure for different spacetimes because the lightcones characterizing them are in different spacetimes. If the spacetimes had common coordinates, the comparison would become possible but one cannot assume this.
Hardy proposes what he calls quantum Equivalence Principle (see this). It should be possible at least locally to compare small deformations of spacetime metric by finding coordinates in which the lightcone defining the causal structure coincide.
 The TGD based solution is much simpler. Spacetimes are identified as 4surfaces in H=M^{4}× CP_{2} and subset of preferred coordinate for H  Minkowski coordinates when the M^{4} projection of spacetime surface is 4D  provides universal spacetime coordinates and one can compare spacetime surfaces and their induced causal structure. In quantum sector the second quantized free spinor fields in H can be restricted to spacetime surface and define fermionic propagators and causal structure.
The important point is that the configurations AB and BA appearing in quantum switch corresponds to a spacetime surface represents a branching of 3surfaces representing photon propagation to two pieces at beam splitter and recombination back to single 3surface making it possible for the photon wave functions interfere. Causal indefiniteness in the proposed sense does not mean that the direction of the causal arrow as an arrow of time is changed and in TGD framework it is not natural to speak about causal indefiniteness.
See the chapter Topological Quantum Computation in TGD Universe or the article Still about the notion of causal indefiniteness in TGD framework.
