Mutual Unbiasedness in Coarse-grained Continuous Variables
Abstract
The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.
Cite
@article{arxiv.1709.00137,
title = {Mutual Unbiasedness in Coarse-grained Continuous Variables},
author = {Daniel S. Tasca and Piero Sánchez and Stephen P. Walborn and Łukasz Rudnicki},
journal= {arXiv preprint arXiv:1709.00137},
year = {2018}
}
Comments
5 pages, 3 figures + Supplemental Material (1 page) v2: Introduction expanded, minor typos corrected