Optimal Probabilistic Simulation of Quantum Channels from the Future to the Past

Abstract

We introduce the study of quantum protocols that probabilistically simulate quantum channels from a sender in the future to a receiver in the past. The maximum probability of simulation is determined by causality and depends on the amount and type (classical or quantum) of information that the channel can transmit. We illustrate this dependence in several examples, including ideal classical and quantum channels, measure-and-prepare channels, partial trace channels, and universal cloning channels. For the simulation of partial trace channels, we consider generalized teleportation protocols that take N input copies of a pure state in the future and produce M < N output copies of the same state in the past. In this case, we show that the maximum probability of successful teleportation increases with the number of input copies, a feature that was impossible in classical physics. In the limit of asymptotically large N, the probability converges to the probability of simulation for an ideal classical channel. Similar results are found for universal cloning channels from N copies to M > N approximate copies, exploiting a time-reversal duality between universal cloning and partial trace.