There is a decade old quantum erasure configuration which seems to literally allow to send information back in time(?):
We produce two entangled photons - first spin up, second spin down or oppositely.
Photon s comes through double slit on which there are installed two different quarter wave plates changing polarization to circular in two different ways.
Finally there are two possibilities:
x y R L
y x L R
where columns are: linear polarization of p, initial linear polarization of s, circular polarization of s after going through slit 1, circular polarization of s after going through slit 2.
So if we know only the final circular polarization of s, we still don't know which slit was chosen, so we should get interference. But if we additionally know if p is x or y, we would know which slit was chosen and so interference pattern would disappear.
So let us add polarizer on p path - depending on its rotation we can or cannot get required information - rotating it 45deg we choose between classical and interfering behavior of s ... but depending on optical lengths, this choice can be made later ...
Phys. Rev. A paper:
http://grad.physics.sunysb.edu/~amarch/Walborn.pdf
discussion:
http://www.thescienceforum.com/physics/27354-controlled-delayed-quantum-erasure-where-causality.html
What is the problem with something like that?
Time paradox? But we have to remember that it would control just few degrees of freedom. There have left huge amount of thermodynamical dof - they seem random for us, but physics could easily bend them to fulfill some additional time loop-like constrains ... for example making that such channel would lie.