Mutual Unbiasedness in Coarse-Grained Continuous Variables

Tasca, Daniel S.; Sánchez, Piero; Walborn, Stephen P.; Rudnicki, Łukasz

doi:10.1103/PhysRevLett.120.040403

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Mutual Unbiasedness in Coarse-Grained Continuous Variables

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Rudnicki, Łukasz
Quantumness, Tomography, Entanglement, and Codes, Leuchs Division, Max Planck Institute for the Science of Light, Max Planck Society;

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Citation

Tasca, D. S., Sánchez, P., Walborn, S. P., & Rudnicki, Ł. (2018). Mutual Unbiasedness in Coarse-Grained Continuous Variables. Physical Review Letters, 120(4): 040403. doi:10.1103/PhysRevLett.120.040403.

Cite as: https://hdl.handle.net/21.11116/0000-0000-D426-6

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.