This question is discussed in the latest episode of Through the Wormhole with Morgan Freeman, the television science documentary series produced for the Discovery Channel.
One of the scientists at the forefront of this research is Professor Sandu Popescu from the School of Physics, University of Bristol.
Together with Morgan Freeman he describes one of the quantum paradoxes that he and his collaborators discovered, namely the Quantum Pigeonhole Principle in which three microscopic particles, such as atoms or molecules, can be put in two boxes but no two particles are in the same box!
To find out how this is possible and what this has to say about going back in time, watch the documentary - the link below takes you to YouTube.
Through the Wormhole, season 6 episode 2: Can Time Go Backwards?