Entropic uncertainty relations for successive measurements in the presence of a minimal length
arXiv:1805.11253 · doi:10.3390/e20050354
Abstract
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the Rényi and Tsallis types. Here, specific features of measurements of observables with continuous spectra should be taken into account. First, we formulated uncertainty relations in terms of Shannon entropies. Since such relations involve a state-dependent correction term, they generally differ from preparation uncertainty relations. This difference is revealed when position is measured by the first. In contrast, state-independent uncertainty relations in terms of Rényi and Tsallis entropies are obtained with the same lower bounds as in the preparation scenario. These bounds are explicitly dependent on the acceptance function of apparatuses in momentum measurements. Entropic uncertainty relations with binning are discussed as well.
12 pages, no figures. Differs in style from the journal version. Published in Entropy as part of the Special Issue "Quantum Foundations: 90 Years of Uncertainty"
References in corpus (19)
- Stronger uncertainty relations for the sum of variances
- Formulation of the uncertainty relations in terms of the Renyi entropies
- GRBs Neutrinos as a Tool to Explore Quantum Gravity induced Lorentz Violation
- Equivalence of wave-particle duality to entropic uncertainty
- Reverse Reconciliation Continuous Variable Quantum Key Distribution Based on the Uncertainty Principle
- Majorization approach to entropic uncertainty relations for coarse-grained observables
- Rényi entropy uncertainty relation for successive projective measurements
- The Most General Form of Deformation of the Heisenberg Algebra from the Generalized Uncertainty Principle
- Coherence and entanglement measures based on Rényi relative entropies
- Incorporation of Generalized Uncertainty Principle into Lifshitz Field Theories
- A revision of the Generalized Uncertainty Principle
- Entropic uncertainty relations for successive measurements of canonically conjugate observables
- On entropic uncertainty relations in the presence of a minimal length
- The world according to Renyi: Thermodynamics of multifractal systems
- The minimal length and the Shannon entropic uncertainty relation
- Quantum preparation uncertainty and lack of information
- Entropic uncertainty relations for successive generalized measurements
- Uncertainty relation based on Wigner-Yanase-Dyson skew information with quantum memory
- Entropic uncertainty relation based on generalized uncertainty principle