English
Related papers

Related papers: Uncertainty Relation for a Single Observable

200 papers

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 derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems. The relations are formulated in terms of a directly operational…

Quantum Physics · Physics 2014-02-28 Joseph M. Renes , Volkher B. Scholz

The well-known Robertson-Schroedinger uncertainty relations miss an irreducible lower bound. This is widely attributed to the lower bound's state-dependence. Therefore, Abbott \emph{et al.} introduced a general approach to derive tight…

Quantum Physics · Physics 2020-10-14 Stephan Sponar , Armin Danner , Kazuma Obigane , Simon Hack , Yuji Hasegawa

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

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

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

Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…

Quantum Physics · Physics 2017-06-27 Alberto Barchielli , Matteo Gregoratti , Alessandro Toigo

We consider uncertainty relations that give lower bounds to the sum of variances. Finding such lower bounds is typically complicated, and efficient procedures are known only for a handful of cases. In this paper we present procedures based…

Quantum Physics · Physics 2019-05-29 Paolo Giorda , Lorenzo Maccone , Alberto Riccardi

Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…

Quantum Physics · Physics 2007-05-23 Adam Azarchs

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of…

Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…

Quantum Physics · Physics 2026-05-29 Iwo Bialynicki-Birula , Zofia Bialynicka-Birula

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

We construct uncertainty relation for arbitrary finite dimensional PT invariant non-Hermitian quantum systems within a special inner product framework. This construction is led by good observables which are a more general class of…

Quantum Physics · Physics 2023-04-11 Namrata Shukla , Ranjan Modak , Bhabani Prasad Mandal

We analyze the weak and critical points of various uncertainty relations that follow from the inequalities for the norms of vectors in the Hilbert space of states of a quantum system. There are studied uncertainty relations for sums of…

Quantum Physics · Physics 2025-08-13 Krzysztof Urbanowski

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

Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this…

Quantum Physics · Physics 2018-07-31 Jun Feng , Yao-Zhong Zhang , Mark D. Gould , Heng Fan

Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…

Quantum Physics · Physics 2023-02-16 Md. Manirul Ali

Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased…

Quantum Physics · Physics 2026-04-08 Baolong Cheng , Zhaoqi Wu

Entropic uncertainty relations express the quantum mechanical uncertainty principle by quantifying uncertainty in terms of entropy. Central questions include the derivation of lower bounds on the total uncertainty for given observables, the…

Quantum Physics · Physics 2012-02-02 Sönke Niekamp , Matthias Kleinmann , Otfried Gühne

The Wigner-Yanase skew information stands for the uncertainty about the information on the values of observables not commuting with the conserved quantity. The Wigner-Yanase skew information-based uncertainty relations can be regarded as a…

Quantum Physics · Physics 2024-05-21 Qing-Hua Zhang , Shao-ming Fei