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Entropic uncertainty relations and their applications

Patrick J. Coles, Mario Berta, Marco Tomamichel +1 more

The Heisenberg uncertainty principle has a more precise formulation in terms of inequalities involving quantum entropies. Currently known entropic uncertainty relations are presented; they capture and extend Heisenberg's idea of the unpredictability of the outcomes of incompatible measurements. Distinct results are obtained for finite- and infinite-dimensional Hilbert spaces. Applications are surveyed, including the formulation of entanglement witnesses, current ideas about wave-particle duality, and the analysis of quantum cryptography.The Heisenberg uncertainty principle has a more precise formulation in terms of inequalities involving quantum entropies. Currently known entropic uncertainty relations are presented; they capture and extend Heisenberg's idea of the unpredictability of the outcomes of incompatible measurements. Distinct results are obtained for finite- and infinite-dimensional Hilbert spaces. Applications are surveyed, including the formulation of entanglement witnesses, current ideas about wave-particle duality, and the analysis of quantum cryptography.

arXiv:1511.04857Reviews of Modern PhysicsFeb 6, 2017664 citations

On the entropic formulation of uncertainty for quantum measurements

Franklin E. Schroeck

The formulation of the uncertainty principle based on entropy is given with the (noncommuting) observables described via positive operator-valued measures.

Journal of Mathematical PhysicsSep 1, 198914 citations

Uncertainty, Entropy, and the Statistical Mechanics of Microscopic Systems

R. Blankenbecler, M. Hossein Partovi

Noting that quantum measurements are in general incomplete, we develop, starting from a recent entropic formulation of uncertainty, a maximum uncertainty principle to define the statistical mechanics of microscopic systems. The resulting ensemble entropy coincides with the expression of von Neumann, thus providing a unified, quantum basis for statistical physics of all systems. Examples involving momentum and position measurements are discussed.

Physical Review LettersFeb 4, 198545 citations

Entropic uncertainty relation for successive measurements

Kyunghyun Baek, Wonmin Son

In quantum mechanics, the uncertainty is fundamental concept, so its underlying meaning has been argued intensively due to its weird properties. On this account, there has been various fomulations expressing the uncertainty principle in dierent ways. In this paper, the new entropic uncertainty relations will be suggested showing dierent aspects of uncertainty as we consider successive measurements. Already, Deutsch and Unk suggested entropic uncertainty relations, so our work will be to modify it as focusing on another aspect (error-disurbance) of uncertainry. The uncertainty relations Heisenberg is the rst man who suggested the uncertainty principle. In 1927 [1], he proposed the uncertainty relation,In quantum mechanics, the uncertainty is fundamental concept, so its underlying meaning has been argued intensively due to its weird properties. On this account, there has been various fomulations expressing the uncertainty principle in dierent ways. In this paper, the new entropic uncertainty relations will be suggested showing dierent aspects of uncertainty as we consider successive measurements. Already, Deutsch and Unk suggested entropic uncertainty relations, so our work will be to modify it as focusing on another aspect (error-disurbance) of uncertainry. The uncertainty relations Heisenberg is the rst man who suggested the uncertainty principle. In 1927 [1], he proposed the uncertainty relation,

Jan 1, 20120 citations

Relative entropic uncertainty relation

Stefan Floerchinger, Tobias Haas, Ben Hoeber

Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied directly to observables with either discrete or continuous spectra. We find that a sum of relative entropies is bounded from above in a nontrivial way, which we illustrate with some examples.

arXiv:2012.10080Physical Review AJun 4, 202113 citations

An Entropic Uncertainty Principle for Quantum Measurements

M. Krishna, Kalyanapuram Rangachari Parthasarathy

The entropic uncertainty principle as outlined by Maassen and Uffink for a pair of non-degenerate observables in a finite level qusystem is generalized here to the case of a pair of arbitrary quantum measurements. In particular, our result includes not only the case of projectivmeasurements (or equivalently, observables) exhibiting degeneracy but also an uncertainty principle for a single measurement.

arXiv:quant-ph/0110025Oct 4, 200137 citations

Entropic Formulation of Uncertainty for Quantum Measurements

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Entropic Formulation of Uncertainty for Quantum Measurements

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