Formulation of the uncertainty relations in terms of the Renyi entropies

Details Formulation of the uncertainty relations in terms of the Renyi entropies Formulation of the uncertainty relations in terms of the Renyi entropies

2006-08-14

arxiv.org/abs/quant-ph/0608116v2

Phys. Rev. A 74, 052101 (2006)

Physics

Quantum Physics

Scientific paper

10.1103/PhysRevA.74.052101

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.

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