Mutual Unbiasedness in Coarse-Grained Continuous Variables

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Tasca D.S.
Sánchez P.
Walborn S.P.
Rudnicki Ł.
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American Physical Society
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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.
We would like to thank A. Z. Khoury and U. Seyfarth for helpful discussions. D. S. T. and P. S. also thank A. Z. Khoury for the access to Lab facilities. The authors acknowledge financial support from the Brazilian funding agencies CNPq, CAPES, FAPERJ, and the National Institute of Science and Technology for Quantum Information. P. S. acknowledges financial support by Grant No. 233-2015 from CONCYTEC-FONDECYT, Peru. Ł. R. acknowledges financial support by Grant No. 2014/13/D/ST2/01886 of the National Science Center, Poland.
Palabras clave
Quantum theory, Coarse Graining, Coarse-grained, Coarse-grained measurements, Conjugate variables, Continuous variable system, Fraunhofer diffraction, Diffraction