Proposal for a Time Loop Experiment, for a Time Loop Quantum Teleportation, and/or a Corresponding Slight Extension of the No-cloning Theorem

Abstract

Using the usual simplified quantum teleportation theory of Bennett et al. we describe a scheme to teleport an unknown quantum multiple times and combine this scheme with results from special relativity. This would yield the prediction that it is possible to teleport an arbitrary unknown quantum state within an experimental setup with given probability to a point slightly within the past of the starting point. Using these results we give a theoretical proposal for that what one might call a time loop experiment with photons. The polarization state of a photon is teleported to a far distant location with given probability, and from there within a second quantum teleportation setup, which moves with high speed in direction to the distant point, back close to the starting point with given probability. Due to special relativity, for a suitable experimental setup, the final photon would be close to the starting point, however, slightly in the past of it. Using appropriate moving and non‐moving mirrors the frequency of the latter photon might be shifted so that it equals that of the starting photon. The polarization phase of the final photon could be shifted using non‐moving mirrors. Then the final photon might be used as input instead of the original photon completing in principle a space time loop. Adjusting the time loop parameters in a certain way, and including some transformations, an in principle instantaneous quantum teleportation with in principle 100% success rate might be achieved. The experiment would lead to a very slight extension of the no‐cloning theorem: an arbitrary unknown quantum cannot be cloned, except within certain time loop experiments. The original no‐cloning theorem would remain almost unchanged, because we cannot ascertain a cloned unknown state in the time loop experiment, and therefore, we cannot use these special clones, as it is well known, to transmit classical information superluminally, and we cannot transmit it into the past. The extension of the no‐cloning theorem would be due to the fact that special relativity is taken into account in our analysis. Further extensions of the experiments are described, and the results are discussed. The case that the accuracy necessary for these loop experiments cannot be achieved practically is discussed. This might lead to interesting effects, e.g. to a suppression of the generation of EPR‐pairs, which yields that the corresponding photon detectors do not detect such photons. An analysis beyond this usual quantum teleportation and relativity theory which will include quantum field theory remains to be conducted in future.