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The Schr{\"o}dinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such, it can yield a stricter separability…

Quantum Physics · Physics 2009-11-13 Hyunchul Nha

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 describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…

Quantum Physics · Physics 2016-01-26 Jinchuan Hou , Kan He

New sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. One of consequences is the new inequality, giving a nonzero lower bound for the…

Quantum Physics · Physics 2018-02-14 V. V. Dodonov

The generalized uncertainty connection between the fluctuations of a quantum observable and its temporal derivative is derived in this study, we demonstrate that the product of an observable's uncertainties and its time derivative is…

Quantum Physics · Physics 2025-08-26 Tarek Yehia

Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…

Quantum Physics · Physics 2026-05-27 Haruki Yamashita , Aina Mayumi , Gen Kimura

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

Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises,…

Quantum Physics · Physics 2007-05-23 Gordon N. Fleming

A new lower boundary for the product of variances of two observables is obtained in the case, when these observables are entangled with the third one. This boundary can be higher than the Robertson--Schr\"odinger one. The special case of…

Quantum Physics · Physics 2017-11-13 V. V. Dodonov

Uncertainty relation is one of the fundamental building blocks of quantum theory. Nevertheless, the traditional uncertainty relations do not fully capture the concept of incompatible observables. Here we present a stronger…

Quantum Physics · Physics 2017-01-05 Qiu-Cheng Song , Cong-Feng Qiao

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 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

We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schr\"{o}dinger-type uncertainty relations are provided. These new lower…

Quantum Physics · Physics 2016-08-23 Bin Chen , Ning-Ping Cao , Shao-Ming Fei , Gui-Lu Long

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

Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…

Quantum Physics · Physics 2015-01-07 Lorenzo Maccone , Arun K. Pati

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

We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…

Quantum Physics · Physics 2026-04-16 Krzysztof Urbanowski

Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an…

Quantum Physics · Physics 2023-08-01 Xiaoli Hu , Naihuan Jing

The canonical Robertson-Schr\"{o}dinger uncertainty relation provides a loose bound for the product of variances of two non-commuting observables. Recently, several tight forward and reverse uncertainty relations have been proved which go…

Quantum Physics · Physics 2020-05-06 Lei Xiao , Bowen Fan , Kunkun Wang , Arun Kumar Pati , Peng Xue

We develop a new abstract derivation of the observability inequalities at two points in time for Schr\"odinger type equations. Our approach consists of two steps. In the first step we prove a Nazarov type uncertainty principle associated…

Analysis of PDEs · Mathematics 2019-11-07 Shanlin Huang , Avy Soffer
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