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Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…

Quantum Physics · Physics 2017-05-25 Qiu-Cheng Song , Jun-Li Li , Guang-Xiong Peng , Cong-Feng Qiao

Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…

Quantum Physics · Physics 2022-05-25 Yunlong Xiao , Naihuan Jing , Bing Yu , Shao-Ming Fei , Xianqing Li-Jost

We show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty…

Quantum Physics · Physics 2022-02-02 Shao-Hen Chiew , Manuel Gessner

Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6,…

Quantum Physics · Physics 2016-12-30 Kamal Bhattacharyya

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…

Quantum Physics · Physics 2020-03-16 Ilya Kull , Philippe Allard Guérin , Frank Verstraete

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

The products of weak values of quantum observables are shown to be of value in deriving quantum uncertainty and complementarity relations, for both weak and strong measurement statistics. First, a 'product representation formula' allows the…

Quantum Physics · Physics 2016-06-08 Michael J. W. Hall , Arun Kumar Pati , Junde Wu

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 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

Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…

Quantum Physics · Physics 2025-08-05 M. Y. Abd-Rabbou , Cong-Feng Qiao

Aharonov's weak value, which is a physical quantity obtainable by weak measurement, admits amplification and hence is deemed to be useful for precision measurement. We examine the significance of the amplification based on the uncertainty…

Quantum Physics · Physics 2016-07-22 Jaeha Lee , Izumi Tsutsui

Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…

Quantum Physics · Physics 2023-05-30 Alexey E. Rastegin

Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…

Quantum Physics · Physics 2015-05-12 Qiu-Cheng Song , Cong-Feng Qiao

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

In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…

Quantum Physics · Physics 2014-05-28 Paul Busch , David B Pearson

In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…

Probability · Mathematics 2020-06-16 Xinjia Chen

Quantum multiparameter estimation focuses on the simultaneous inference of multiple parameters in quantum systems through measurement and data processing. Its complexity stems from two key factors: measurement incompatibility and parameter…

Quantum Physics · Physics 2025-09-15 Bing-Shu Hu , Xiao-Ming Lu

We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…

Quantum Physics · Physics 2016-01-18 Reinhard F. Werner

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

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