Renyi Entropy and the Uncertainty Relations

Journal Article · Wed Feb 21 00:00:00 EST 2007 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2713446· OSTI ID:21054921

Bialynicki-Birula, Iwo ^[1]

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1. Center for Theoretical Physics, Al. Lotnikow 32/46, 02-668 Warsaw (Poland)

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 Renyi 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 Renyi entropies. The mathematical proofs of all the inequalities discussed in this paper can be found in Phys. Rev. A 74, No. 5 (2006); arXiv:quant-ph/0608116.

• OSTI ID: 21054921
• Journal Information: AIP Conference Proceedings, Vol. 889, Issue 1; Conference: 4. international conference on foundations of probability and physics, Vaexjoe (Sweden), 4-9 Jun 2006; Other Information: DOI: 10.1063/1.2713446; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
ENERGY LEVELS
ENTROPY
MIXED STATE
QUANTUM MECHANICS
UNCERTAINTY PRINCIPLE