Abstract
The Heisenberg-Robertson uncertainty relation is the hallmark of quantum physics and has been widely investigated. However, it does not capture the concept of incompatible observables because it can be trivial even for incompatible observables. Recently some stronger uncertainty relations relating the sums of variances were proposed. Here we experimentally demonstrate that these stronger multiobservable uncertainty relations are valid in a state-dependent manner and that the lower bound is guaranteed to be nontrivial for multiple observables that are incompatible on the state of the system being measured. We find that the behavior of multiple high-dimensional observables agrees with the predictions of quantum theory. Our experimental results not only foster insight into a fundamental limitation of measurements with multiple observables but also contribute to the study of the precision measurement technology in quantum information processing.
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