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首页> 美国卫生研究院文献>Entropy >Entropic Uncertainty Relations for Successive Measurements in the Presence of a Minimal Length
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Entropic Uncertainty Relations for Successive Measurements in the Presence of a Minimal Length

机译：在最小长度存在下连续测量的熵不确定性关系

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We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. Here, specific features of measurements of observables with continuous spectra should be taken into account. First, we formulated uncertainty relations in terms of Shannon entropies. Since such relations involve a state-dependent correction term, they generally differ from preparation uncertainty relations. This difference is revealed when the position is measured by the first. In contrast, state-independent uncertainty relations in terms of Rényi and Tsallis entropies are obtained with the same lower bounds as in the preparation scenario. These bounds are explicitly dependent on the acceptance function of apparatuses in momentum measurements. Entropic uncertainty relations with binning are discussed as well.

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