Contradictory uncertainty relations

Abstract

We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get that the minimum uncertainty states of some uncertainty relations are the maximum uncertainty states of closely related uncertainty relations, and vice versa.

4 pages, 10 figures

References in corpus (4)

• Formulation of the uncertainty relations in terms of the Renyi entropies
• Local and Global Distinguishability in Quantum Interferometry
• Some extensions of the uncertainty principle
• Entropic uncertainty relations for extremal unravelings of super-operators

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• On a generalized entropic uncertainty relation in the case of the qubit
• Alternative measures of uncertainty in quantum metrology: Contradictions and limits
• Entropic measures of joint uncertainty: effects of lack of majorization
• A geometric formulation of uncertainty principle
• Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures
• Nonclassical states from the joint statistics of simultaneous measurements
• Information and quantum theories: an analysis in one-dimensional systems
• Sub-Poissonian and anti-bunching criteria via majorization of statistics
• A combined-probability space and (un)certainty relations for a finite-level quantum system
• Phase-number uncertainty from Weyl commutation relations