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Entropic uncertainty relations for successive measurements of canonically conjugate observables. (English) Zbl 1357.81022
Summary: Uncertainties in successive measurements of general canonically conjugate variables are examined. Such operators are approached within a limiting procedure of the Pegg-Barnett type. Dealing with unbounded observables, we should take into account a finiteness of detector resolution. An appropriate reformulation of two scenarios of successive measurements is proposed and motivated. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. The Rényi and Tsallis formulations of uncertainty relations are obtained for both the scenarios of successive measurements of canonically conjugate operators. Entropic uncertainty relations for the cases of position and momentum are separately discussed.

MSC:
81P15 Quantum measurement theory, state operations, state preparations
81S05 Commutation relations and statistics as related to quantum mechanics (general)
62J10 Analysis of variance and covariance (ANOVA)
94A17 Measures of information, entropy
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