Granted, I Am Not A Quantum Physicist, but I do have some ideas on how the "rules of the road" in time travel might work.
First and foremost, the old chestnut of the Grandfather Paradox, or any other paradox for that matter. The Universe and most of its subsequent parts
are, by and large, a self-healing organism. We can see this in microcosm here on good ol' Terra Firma in areas that have been left for natural
reclamation after farming, or natural disasters.
Seriously. Check out some of the more recent information on the area around Pripyat, in the Ukraine. 20-someodd years after Chernobyl, and Mother
Nature has made some great strides.
I suspect that even if paradoxes could occur, then the universe would more than likely compensate for it in some fashion, whether by retconning things
to the point where the paradox could not occur (possible explanation for deja vu?), or by treating the paradox like a cancer and eliminating the
problem timeline.
Going backward, I would think, would present several difficulties. One, you have to generate enough energy to fight against the pull of entropy, which
is always trying to move things along. Next, you would have the problem of getting back, reliably.
Quantum theory supposes that multiple timelines branch off from each decision point, each event that occurs, every millisecond of every day. Unless
you could leave a trail of 'breadcrumbs' to follow, or have some other way to determine your relative position in the multiversal sheaf to where you
came from, you could potentially spend the rest of your life hopping the timelines and not get any closer to home. This would impose a requirement for
massive computational ability and data storage, so unless you've got a convenient warehouse to time-travel in, your range would also likely be
limited.
Going forward might be slightly easier, but also presents its own problems. First, you've got the branching timelines again - which one do you
follow? And again, how would you get back? Quantum probability may be of some use here, in that it would help predict what the most 'stable'
iterations of your current timeline would be. Again, big honking computers manned by big honking brains. Energy requirements would likely be lower,
since you're going with the "flow" of entropy as you move forward.
There are some ways that these limitations could be worked around. Quantum entanglement/teleportation comes to my mind, as we've already proven that
two entangled particles mirror each other in space. Time may be another means for it. As far as energy generation goes, there've been a few ideas
about harnessing the power of a singularity - not a huge one, but a smaller one like some say the Large Hadron Collider will spawn. Basically, just
feed it mass, and farm the resulting Hawking energy.
In summary, I think it's possible... I just don't think we have the technology yet to make it a predictable, much less safe or reliable, mode of
exploration.
But again, I am not a physicist, just a wannabe SF author.