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A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…

Quantum Physics · Physics 2009-09-25 G. Rigolin

A survey on the generalizations of Heisenberg uncertainty relation and a general scheme for their entangled extensions to several states and observables is presented. The scheme is illustrated on the examples of one and two states and…

Quantum Physics · Physics 2016-09-08 D. A. Trifonov

Uncertainty relations for light pulses found in [Phys. Rev. A {\bf 86}, 022118 (2012)] were derived in the three-dimensional case which emphasized the localization in a volume. Here we derive the uncertainty relation for light beams in the…

Optics · Physics 2013-11-07 Iwo Bialynicki-Birula , Zofia Bialynicka-Birula

In spite of enormous theoretical and experimental progresses in quantum uncertainty relations, the experimental investigation of most current, and universal formalism of uncertainty relations, namely majorization uncertainty relations…

We give a bound to the precision in the estimation of a parameter in terms of the expectation value of an observable. It is an extension of the Cramer-Rao inequality and of the Heisenberg uncertainty relation, where the estimation precision…

Quantum Physics · Physics 2012-07-11 Vittorio Giovannetti , Seth Lloyd , Lorenzo Maccone

Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…

Quantum Physics · Physics 2026-04-07 Qing-Hua Zhang , Cong Xu , Jing-Feng Wu , Shao-Ming Fei

The Schr{\"o}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is…

Quantum Physics · Physics 2020-08-10 Jaeha Lee , Keita Takeuchi , Kaisei Watanabe , Izumi Tsutsui

Uncertainty and intrinsic measurement disturbance, two fundamental concepts in quantum measurement, have conventionally been viewed as distinct and studied separately. In this work, we establish a fundamental connection between them,…

Quantum Physics · Physics 2026-04-21 Liang-Liang Sun , Kishor Bharti , Xiang Zhou , Leong-Chuan Kwek , Jingyun Fan , Sixia Yu

Recently,D.Mondal et.al[Phys. Rev. A. 95, 052117(2017)]creatively introduce a new interesting concept of reverse uncertainty relation which indicates that one cannot only prepare quantum states with joint small uncertainty, but also with…

Quantum Physics · Physics 2023-08-28 Xiao Zheng , Ai-Ling Ji , Guo-Feng Zhang

We prove some isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We then relate them to inequalities involving the higher order mean-curvature integrals. We also apply our…

Differential Geometry · Mathematics 2017-08-23 Kwok-Kun Kwong

We provide a unified and strengthened framework for the product form and the sum form variance-based uncertainty relations by constructing a unified uncertainty relation. In the unified framework, we deduce that the uncertainties of the…

Quantum Physics · Physics 2020-02-24 Xiao Zheng , Shao-Qiang Ma , Guo-Feng Zhang , Heng Fan , Wu-Ming Liu

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the…

Quantum Physics · Physics 2011-09-12 Iwo Bialynicki-Birula , Lukasz Rudnicki

Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the…

Quantum Physics · Physics 2026-05-05 Alberto Riccardi , Lorenzo Maccone

In this paper we obtain some new Schwarz related inequalities in inner product spaces over the real or complex number field. Applications for the generalized triangle inequality are also given.

Metric Geometry · Mathematics 2007-05-23 Sever Silvestru Dragomir

The Guide to the Expression of Uncertainty in Measurement (GUM) mainly deals with measurement models having only a single output quantity. However, in many cases more than one output quantity is required, where all of them are related to a…

Data Analysis, Statistics and Probability · Physics 2011-04-29 Michael P. Krystek

We establish tighter uncertainty relations for arbitrary finite observables via $(\alpha,\beta,\gamma)$ weighted Wigner-Yanase-Dyson ($(\alpha,\beta,\gamma)$WWYD) skew information. The results are also applicable to the $(\alpha,\gamma)$…

Quantum Physics · Physics 2024-05-21 Cong Xu , Zhaoqi Wu , Shao-Ming Fei

We present an equivalence theorem to unify the two classes of uncertainty relations, i.e., the variance-based ones and the entropic forms, which shows that the entropy of an operator in a quantum system can be built from the variances of a…

Quantum Physics · Physics 2016-12-13 Jun-Li Li , Cong-Feng Qiao

We show within a very simple framework that different measures of fluctuations lead to uncertainty relations resulting in contradictory conclusions. More specifically we focus on Tsallis and Renyi entropic uncertainty relations and we get…

Quantum Physics · Physics 2011-09-19 Alfredo Luis

Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…

Quantum Physics · Physics 2015-02-24 Petr Jizba , Jacob A. Dunningham , Jaewoo Joo

We prove uncertainty relations that quantitatively express the impossibility of jointly sharp preparation of pre- and post-selected quantum states for measuring incompatible observables during the weak measurement. By defining a suitable…

Quantum Physics · Physics 2014-11-27 Arun Kumar Pati , Junde Wu