SAMOP 2023 – scientific programme

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QI: Fachverband Quanteninformation

QI 2: Quantum Foundations

QI 2.5: Talk

Monday, March 6, 2023, 12:00–12:15, B302

Distribution of quantum incompatibility across subsets of multiple measurements — •Lucas Tendick, Hermann Kampermann, and Dagmar Bruß — Institute for Theoretical Physics, Heinrich Heine University Düsseldorf, D-40225 Düsseldorf, Germany

The incompatibility of quantum measurements, i.e., the impossibility of measuring two or more observable quantities simultaneously, is one of the most fundamental properties of quantum physics. Not only are incompatible measurements necessary to reveal nonlocal effects, such as quantum steering and the violation of Bell inequalities, but they are also valuable resources that provide advantages in various information processing tasks. It is generally known that increasing the number of distinct measurements can also increase the incompatibility. However, it is yet unknown how much incompatibility can be gained from adding more measurements to an existing measurement scheme and on what this gain depends. Here, we show how the maximal incompatibility that can be gained by increasing the number of measurements can be upper bounded by functions of the incompatibility of respective subsets of the available measurements. More generally, we show how to bound the incompatibility of a set of measurements using the properties of its subsets, which reveals a new notion of measurement incompatibility. We prove the relevance of our bounds by providing tight examples using noisy measurements based on mutually unbiased bases. Finally, we discuss the direct consequences of our results for the nonlocality that could be gained by increasing the number of measurements in a Bell experiment.