Formulation of the uncertainty relations in terms of the Renyi entropies

Abstract

Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the Fourier transformation derived by Babenko and Beckner. Analogous uncertainty relations are derived for angle and angular momentum and also for a pair of complementary observables in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Renyi entropies.

References in corpus (14)

• Matrix product states represent ground states faithfully
• Extremal entanglement and mixedness in continuous variable systems
• An information-theoretic security proof for QKD protocols
• Entropic uncertainty relations and entanglement
• Conceptual Inadequacy of the Shannon Information in Quantum Measurements
• Direct measurement of non-linear properties of bipartite quantum states
• On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
• Renyi-Wehrl entropies as measures of localization in phase space
• An elementary formula for entanglement entropies of fermionic systems
• A generalized skew information and uncertainty relation
• Additivity properties of a Gaussian Channel
• Event by Event Analysis and Entropy of Multiparticle Systems
• Moments of Wigner function and Renyi entropies at freeze-out
• Uniformity of the phase space and fluctuations in thermal equilibrium

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