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- Title
On Entropic Uncertainty Relations for Measurements of Energy and Its "Complement".
- Authors
Rastegin, Alexey E.
- Abstract
Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays an important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is well known that the case of energy and time principally differs from more familiar examples of two non‐commuting observables. Since quantum theory was originated, many approaches to energy–time uncertainties have been proposed. Entropic way to formulate the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, uncertainty relations of the "energy–time" type are obtained in terms of Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state‐dependent and state‐independent formulations are of interest. Some of the derived state‐independent bounds are similar to the results obtained within a more general approach on the basis of sandwiched relative entropies. The developed method allows us to address the case of detection inefficiencies. No consensus exists on formulation of uncertainty relations for energy and time, despite their heuristic role. Using the notion of Hamiltonian complement, entropic uncertainty relations of the "energy–time" type are treated similarly to the case of usual observables. Within their scope, the derived relations realize advantages of entropic approach to the uncertainty principle.
- Subjects
ENTROPIC uncertainty; STATISTICAL physics; HEISENBERG uncertainty principle; ENERGY measurement; QUANTUM theory; QUANTUM information science
- Publication
Annalen der Physik, 2019, Vol 531, Issue 4, pN.PAG
- ISSN
0003-3804
- Publication type
Article
- DOI
10.1002/andp.201800466