Formulation of the uncertainty relations in terms of the Renyi entropies

Journal Article · Wed Nov 15 00:00:00 EST 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.052101· OSTI ID:20974680

Bialynicki-Birula, Iwo ^[1]

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

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.

• OSTI ID: 20974680
• Journal Information: Physical Review. A, Vol. 74, Issue 5; Other Information: DOI: 10.1103/PhysRevA.74.052101; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANGULAR MOMENTUM
ENTROPY
FOURIER TRANSFORMATION
QUANTUM MECHANICS
UNCERTAINTY PRINCIPLE