Entropic measures of joint uncertainty: effects of lack of majorization

Abstract

We compute Rényi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty measure used. These results are not reproduced by a more standard duality relation. We show that these behaviors are consistent with the lack of majorization relation between the corresponding statistics.

10 pages, 3 figures

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Cited by in corpus (9)

• Rényi, Shannon and Tsallis entropies of Rydberg hydrogenic systems
• Optimal common resource in majorization-based resource theories
• Approximate transformations of bipartite pure-state entanglement from the majorization lattice
• Nonclassical states from the joint statistics of simultaneous measurements
• Entropic uncertainty relations for successive measurements in the presence of a minimal length
• Coherence for vectorial waves and majorization
• Extremum-entropy-based Heisenberg-like uncertainty relations
• Majorization of quantum polarization distributions
• Phase-number uncertainty from Weyl commutation relations