Maybe we can look at the coarse-graining due to experimental resolution and see how it can be looked at as weak measurements and whether reversing could be done? I found this on arxiv
http://arxiv.org/abs/0803.3267, but it looks a bit abstract. Do you know if something similar has been done already by someone?
Also, Dr Lee and I have discussed about the first paper and we thought that maybe the inequality does not hold when the conditioning is imposed, i.e., their starting point is invalid. The result of Cabello (ref [6] in the paper) already indicates this and it seems that the paper is just an example, albeit a clever one because they connect the conditioning to an experimental imperfection. Could anyone comment on this please?