Unobservable causal loops as a way to explain both the quantum computational speedup and quantum nonlocality

Abstract

We consider the reversible processes between two one-to-one correlated measurement outcomes which underlie both problem solving and quantum nonlocality. In the former case, the two outcomes are the setting and the solution of the problem; in the latter, they are those of measuring a pair of maximally entangled observables whose subsystems are space separate. We argue that the quantum description of these processes mathematically describes the correlation but leaves the causal structure that physically ensures it free of violating the time symmetry required of the description of a reversible process. It would therefore be incomplete and could be completed by time symmetrizing it. This is done by assuming that the two measurements evenly contribute to selecting the pair of correlated measurement outcomes. Time symmetrization leaves the ordinary quantum description unaltered but shows that it is the quantum superposition of unobservable time-symmetrization instances whose causal structure is completely defined. Each instance is a causal loop: Causation goes from the initial to the final measurement outcome and then back from the final to the initial outcome. In the speedup, all is as if the problem solver knew in advance half of the information about the solution she will produce in the future and could use this knowledge to produce the solution with fewer computation steps. In nonlocality, the measurement on either subsystem retrocausally and locally changes the state of both subsystems when the two were not yet spatially separate. This locally causes the correlation between the two future measurement outcomes.