Shannon entropy as a measure of uncertainty in positions and momenta |
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Authors: | Łukasz Rudnicki |
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Affiliation: | 1.Center for Theoretical Physics,Polish Academy of Sciences Aleja Lotników 32/46,Warsaw,Poland |
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Abstract: | I start with a brief report of the topic of entropic uncertainty relations for the position and momentum variables. Then I investigate the discrete Shannon entropies related to the case of a finite number of detectors set to measure the probability distributions in the position and momentum spaces. I derive the uncertainty relation for the sum of the Shannon entropies which generalizes the previous approach by I. Bialynicki-Birula based on an infinite number of detectors (bins). |
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