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Related papers: The Optimal Uncertainty Relation

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We derive explicit bounds for the average entropy characterizing measurements of a pure quantum state of size $N$ in $L$ orthogonal bases. Lower bounds lead to novel entropic uncertainty relations, while upper bounds allow us to formulate…

We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive.…

Quantum Physics · Physics 2018-03-28 Rene Schwonnek

To find the essential nature of quantum theory has been an important problem for not only theoretical interest but also applications to quantum technologies. In those studies on quantum foundations, the notion of uncertainty plays a primary…

Quantum Physics · Physics 2022-03-01 Ryo Takakura

In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…

Quantum Physics · Physics 2018-06-08 Tom Bullock , Paul Busch

Unsolved controversies about uncertainty relations and quantum measurements still persists nowadays. They originate around the shortcomings regarding the conventional interpretation of uncertainty relations. Here we show that the respective…

Quantum Physics · Physics 2007-05-23 S. Dumitru

This paper concerns the study of optimal (supremum and infimum) uncertainty bounds for systems where the input (or prior) probability measure is only partially/imperfectly known (e.g., with only statistical moments and/or on a coarse…

Machine Learning · Computer Science 2023-01-02 Xingsheng Sun , Burigede Liu

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…

Mathematical Physics · Physics 2018-03-02 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can…

Quantum Physics · Physics 2015-05-06 Shang Liu , Liang-Zhu Mu , Heng Fan

Introductory courses on quantum mechanics usually include lectures on uncertainty relations, typically the inequality derived by Robertson and, perhaps, other statements. For the benefit of the lecturers, we present a unified approach --…

Quantum Physics · Physics 2023-12-18 Berthold-Georg Englert

Entropic uncertainty relations in a finite dimensional Hilbert space are investigated. Making use of the majorization technique we derive explicit lower bounds for the sum of R\'enyi entropies describing probability distributions associated…

Quantum Physics · Physics 2015-11-20 Zbigniew Puchała , Łukasz Rudnicki , Karol Życzkowski

The numerical technique of Lattice QCD holds the promise of connecting the nuclear forces, nuclei, the spectrum and structure of hadrons, and the properties of matter under extreme conditions with the underlying theory of the strong…

Nuclear Theory · Physics 2015-06-23 Silas R. Beane , William Detmold , Kostas Orginos , Martin J. Savage

Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…

Quantum Physics · Physics 2012-02-02 Sönke Niekamp , Matthias Kleinmann , Otfried Gühne

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide…

Quantum Physics · Physics 2021-07-28 Yichen Huang

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…

Quantum Physics · Physics 2013-05-29 Yu Watanabe , Takahiro Sagawa , Masahito Ueda

We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…

Quantum Physics · Physics 2018-11-14 Zhihua Chen , Zhihao Ma , Yunlong Xiao , Shao-Ming Fei

Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the…

Quantum Physics · Physics 2022-11-01 Dong Wang , Fei Ming , Ming-Liang Hu , Liu Ye

Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty…

Quantum Physics · Physics 2017-10-24 Zhih-Ahn Jia , Yu-Chun Wu , Guang-Can Guo

We prove a new sum uncertainty relation in quantum theory which states that the uncertainty in the sum of two or more observables is always less than or equal to the sum of the uncertainties in corresponding observables. This shows that the…

Quantum Physics · Physics 2009-11-13 A. K. Pati , P. K. Sahu

We consider the question of entropic uncertainty relations for prime power dimensions. In order to improve upon such uncertainty relations for higher dimensional quantum systems, we derive a tight lower bound amount of entropy for multiple…

Quantum Physics · Physics 2011-10-03 Jakob Funder

An analysis of quantum measurement is presented that relies on an information-theoretic description of quantum entanglement. In a consistent quantum information theory of entanglement, entropies (uncertainties) conditional on measurement…

Quantum Physics · Physics 2008-02-03 N. J. Cerf , C. Adami