Time-entanglement phenomenon
Time-entanglement means that quantum information from the past may be teleported into the future without actually being present in the interval between. However, teleportation of one qubit requires two classical bits and one EPR pair, and these must exist in the interval, so there is no saving of space: you need to get half of the EPR pair and both classical bits into the future, and that requires a qubit's worth of quantum memory. So this process does not effect complexity classes.