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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

For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…

Quantum Physics · Physics 2018-05-18 Aniello Fedullo

The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial…

Quantum Physics · Physics 2016-05-25 Kunkun Wang , Xiang Zhan , Zhihao Bian , Jian Li , Yongsheng Zhang , Peng Xue

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…

Quantum Physics · Physics 2021-06-07 Stefan Floerchinger , Tobias Haas , Ben Hoeber

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty…

Quantum Physics · Physics 2019-04-10 Zhi-Xin Chen , Hui Wang , Jun-Li Li , Qiu-Cheng Song , Cong-Feng Qiao

We study the Schr\"odinger-Robertson uncertainty relations in an algebraic framework. Moreover, we show that some specific commutation relations imply new equalities, which are regarded as equality versions of well-known inequalities such…

Functional Analysis · Mathematics 2016-10-04 Tohru Ozawa , Kazuya Yuasa

We prove a few novel state-dependent uncertainty relations for product as well the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Roberson-Schr\"odinger uncertainty relation…

Quantum Physics · Physics 2017-05-24 Debasis Mondal , Shrobona Bagchi , Arun Kumar Pati

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

The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…

Quantum Physics · Physics 2026-02-10 Xingze Qiu

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

It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…

Quantum Physics · Physics 2014-01-17 Kazuo Fujikawa

Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…

Quantum Physics · Physics 2009-11-13 Iwo Bialynicki-Birula

We report a refinement of Robertson-Schroedinger uncertainty relation via Wigner-Yanase skew information. Besides the well known quantum uncertainty arising from the noncommutativity of observables, there is classical uncertainty arising…

Quantum Physics · Physics 2013-03-27 Sixia Yu , C. H. Oh

The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…

Quantum Physics · Physics 2009-11-07 Michael J. W. Hall

We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…

Quantum Physics · Physics 2022-01-25 Xiaoli Hu , Naihuan Jing

In this work, we derive Robertson-Heisenberg like uncertainty relation for two incompatible observables in a pre- and post-selected (PPS) system. The newly defined standard deviation and the uncertainty relation in the PPS system have…

Quantum Physics · Physics 2024-01-05 Sahil , Sohail , Sibasish Ghosh

Uncertainty relations for a pair of arbitrary measurements and for a single measurement are posed in the form of inequalities using the Renyi entropies. The formulation deals with discrete observables. Both the relations with…

Quantum Physics · Physics 2008-07-21 A. E. Rastegin

We show that the uncertainty relation as expressed in the Robertson-Schrodinger generalized form can be used to detect the mixedness of three-level quantum systems in terms of measureable expectation values of suitably chosen observables…

Quantum Physics · Physics 2013-03-14 S. Mal , T. Pramanik , A. S. Majumdar

Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…

Quantum Physics · Physics 2018-07-19 Fabricio Toscano , Daniel S. Tasca , Łukasz Rudnicki , Stephen P. Walborn

In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…

Quantum Physics · Physics 2020-05-08 F. Nicacio , F. T. Falciano