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Related papers: Stronger Schr\"odinger-like Uncertainty Relations

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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

We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…

Mathematical Physics · Physics 2009-11-10 Yong Moon Park

The uncertainty principle is one of the characteristic properties of quantum theory based on incompatibility. Apart from the incompatible relation of quantum states, mutually exclusiveness is another remarkable phenomenon in the…

Quantum Physics · Physics 2016-11-09 Yunlong Xiao , Naihuan Jing

We show how the Schroedinger Uncertainty Relation for a pair of observables can be deduced using the Cauchy-Schwarz inequality plus successive applications of the commutation relation involving the two observables. Our derivation differs…

Physics Education · Physics 2015-08-26 Gustavo Rigolin

We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…

Quantum Physics · Physics 2017-04-17 Jun Zhang , Yang Zhang , Chang-shui Yu

For angular observables pairs (angular momentum-angle and number-phase) the adequate reference element of normality is not the Robertson-Schr\"{o}dinger uncertainty relation but a Schwarz formula regarding the quantum fluctuations. Beyond…

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

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

Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…

Quantum Physics · Physics 2012-10-18 Marco Tomamichel , Renato Renner

The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…

Quantum Physics · Physics 2014-02-19 Teiko Heinosaari , Takayuki Miyadera , Daniel Reitzner

As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…

We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…

Quantum Physics · Physics 2024-12-30 Aina Mayumi , Gen Kimura , Hiromichi Ohno , Dariusz Chruściński

Conventional quantum uncertainty relations (URs) contain dispersions of two observables. Generalized URs are known which contain three or more dispersions. They are derived here starting with suitable generalized Cauchy inequalities. It is…

Quantum Physics · Physics 2007-05-23 M. I. Shirokov

We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…

Quantum Physics · Physics 2018-10-03 Sk Sazim , Satyabrata Adhikari , Arun K. Pati , Pankaj Agrawal

We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…

Quantum Physics · Physics 2015-09-24 Bin Chen , Shao-Ming Fei

Uncertainty relations are among the unique fingerprints of quantum physics, being direct expression of non-commutativity and complementarity. Entropic uncertainty relations arise in quantum information theory as the most natural expression…

Quantum Physics · Physics 2014-01-30 Cosmo Lupo , Seth Lloyd

In the present article, we discuss one of the basic relations of Quantum Mechanics - the Uncertainty Relation (UR). In 1930, few years after Heisenberg, Erwin Schrodinger generalized the famous Uncertainty Relation in Quantum Mechanics,…

Quantum Physics · Physics 2008-06-07 A Angelow

In this article, we study the Schr\"odinger equation posed in the Euclidean space. We prove observability inequalities for measurable sets that are thick with respect to decaying densities. The proof relies on quantitative uncertainty…

Analysis of PDEs · Mathematics 2026-02-23 Kévin Le Balc'h , Jiaqi Yu

Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…

Quantum Physics · Physics 2017-09-13 Xiao Yuan , Ge Bai , Tianyi Peng , Xiongfeng Ma

In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…

Quantum Physics · Physics 2015-06-15 Yao Yao , Xing Xiao , Xiaoguang Wang , C. P. Sun

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…