Rényi entropy and the uncertainty relations. (English) Zbl 1139.81302

Białynicki-Birula, Iwo

Adenier, Guillaume (ed.) et al., Foundations of probability and physics – 4, Växjö, Sweden, 4–9 June 2006. Proceedings of the Conference. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0391-8/hbk). AIP Conference Proceedings 889, 52-61 (2007).

Summary: Quantum mechanical uncertainty relations for the position and the momentum and for the angle and the angular momentum are expressed in the form of inequalities involving the Rényi entropies. These uncertainty relations hold not only for pure but also for mixed states. Analogous uncertainty relations are valid also for a pair of complementary observables (the analogs of \(x\) and \(p\)) in \(N\)-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Rényi entropies.
For the entire collection see [Zbl 1115.81004].

MSC:

81P05	General and philosophical questions in quantum theory
81S05	Commutation relations and statistics as related to quantum mechanics (general)
94A17	Measures of information, entropy

Keywords:

uncertainty relations; Rényi entropy; experimental resolution in measurements