Mutual Unbiasedness in Coarse-Grained Continuous Variables

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 e...

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Bibliographic Details
Published in:Physical review letters 2018-01, Vol.120 (4), p.040403-040403, Article 040403
Main Authors: Tasca, Daniel S, Sánchez, Piero, Walborn, Stephen P, Rudnicki, Łukasz
Format: Article
Language:English
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.120.040403