Mutual Unbiasedness in Coarse-grained Continuous Variables

TL;DR

This paper investigates mutual unbiasedness in coarse-grained quantum continuous variables, demonstrating that periodic coarse graining can preserve this property, with theoretical analysis and experimental validation in an optics setup.

Contribution

It introduces a method to maintain mutual unbiasedness in coarse-grained measurements using periodic coarse graining, bridging discrete and continuous quantum mechanics.

Findings

Periodic coarse graining preserves mutual unbiasedness.

Experimental validation with Fraunhofer diffraction matches theory.

Provides a formal link between discrete and continuous quantum systems.

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.