Degradation of a quantum directional reference frame as a random walk

Abstract

We investigate whether the degradation of a quantum directional reference frame through repeated use can be modelled as a classical direction undergoing a random walk on a sphere. We demonstrate that the behaviour of the fidelity for a degrading quantum directional reference frame, defined as the average probability of correctly determining the orientation of a test system, can be fit precisely using such a model. Physically, the mechanism for the random walk is the uncontrollable back-action on the reference frame due to its use in a measurement of the direction of another system. However, we find that the magnitude of the step size of this random walk is not given by our classical model and must be determined from the full quantum description.

Acknowledgements

We wish Peter Knight well on this special occasion and appreciate his support and guidance throughout the years.

The authors gratefully acknowledge J.-C. Boileau, David Poulin, and Robert Spekkens for helpful discussions. SDB acknowledges support from the Australian Research Council (ARC). TR acknowledges support from the Engineering and Physical Sciences Research Council of the United Kingdom, and a University of Sydney Short-Term Visiting Fellowship. BCS acknowledges support from Alberta's Informatics Circle of Research Excellence (iCORE), ARC, and the Canadian Institute for Advanced Research. PST acknowledges support from an iCORE Alberta Ingenuity Fund Fellowship, and from the Network of Centres of Excellence for the Mathematics of Information Technology and Complex systems.