Even if it's possible to create a time machine, it's unlikely that it will be built any time soon.
However, it may be possible to send a single particle back in time. Mathematically, an antiparticle is identical to an ordinary particle travelling back in time. Whether a positron is *actually* an electron travelling back in time, I do not know.
But if it were possible to send a single particle back in time, information (even if just a true/false value) could be sent back in time.
A Turing machine can calculate anything, given enough memory and time.
A computer could be built that upon completing a calculation sends the result back to itself before the calculation begun. This would, in essence, give you unlimited computing power, as any calculation would be performed instantly, without any calculating taking place.
Once it has the answer, it waits a while and then sends it back in time to itself, completing the loop.
The prototype may have broken causality, but fear not, the temporal instabilities have been contained in a safety bauble.