Like classical mechanics, quantum mechanics is a causal theory [1,2]--a theory that forbids sending messages from the future to the past. Still, one can simulate backward communication by postselection.Classically, such simulation is trivial: the receiver has only to guess the value of the message and later the referee will just check if the guess is correct.
The situation is more interesting when the message is quantum. In this case, guessing the message is not an option, since there are infinitely many possibilities. In this talk I will review a recent work  by Lucien Hardy, Dina Genkina, and myself, in which we investigated the optimal simulation of a quantum communication channel backward in time.
In particular, I will show the ultimate bound on the probability of a successful simulation, which follows directly from the causality principle. The bound is tight and, interestingly, it provides an alternative operational interpretation of the conditional min-entropy of a quantum state.
 G. Chiribella, G. M. D’Ariano, and P. Perinotti, Probabilistic Theories with Purification, Phys. Rev. A 81, 062348 (2010)
 G. Chiribella, G. M. D’Ariano, and P. Perinotti, Informational Derivation of Quantum Theory, Phys. Rev. A 84, 012311 (2011)
 D. Genkina, G. Chiribella, and L. Hardy, Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past , Phys. Rev. A 85, 022330 (2012)