Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Change and uncertainty in quantum systems

J. D. Franson

Published Nov 1, 1996• 6 citations
Publisher

Abstract

A simple inequality shows that any change in the expectation value of an observable quantity must be associated with some degree of uncertainty. This inequality is often more restrictive than the Heisenberg uncertainty principle. \textcopyright{} 1996 The American Physical Society.
DOI
10.1103/physreva.54.3808

Related papers

Remarks on Uncertainty Principles

E. U. Condon

Since the publication of Heisenberg’s paper1 on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality, $$ \Delta p\Delta q>\frac{h}{{2\pi}} $$ (1) This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.

Science•May 31, 1929•15 citations

The Wave Function, Expectations Values, and Uncertainty

Nelson Enrique Bolivar, Gabriel Abellán

The uncertainty principle, formulated by Heisenberg in 1927, is a fundamental principle in quantum mechanics. It forces us to review key concepts of classical physics, and from this analysis are born the concepts of quantum physics. Consequences of the Uncertainty principle also introduces the concept of incompatible sizes, a completely new concept compared to classical physics. A state of the system, which we call a quantum state, will be determined from the knowledge of a set maximum of certain quantities that are independent and compatible with each other. A measurable physical quantity is called an observable. If at a given moment a measurement is performed by one or more compatible observables it is said they are performing an observation of the system. The basic principles of quantum mechanics are expressed by a number of postulates. Their numbers and can vary from one text to another.

Apple Academic Press eBooks•May 23, 2018•0 citations

Strict bounds on the Franson inequality

Lev Vaidman A, Ori Belkind

An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)], is analyzed and improved. The inequality connects the change of the expectation value of an observable with the uncertainty of this observable. A strict bound on the ratio between these two quantities is obtained.

arXiv:quant-ph/9707060•Physical Review A•Mar 1, 1998•6 citations

Uncertainty in Quantum Measurements

David Deutsch

The object of this Letter is to show that except in the case of canonically conjugate observables, the generalized Heisenberg inequality does not properly express the quantum uncertainty principle. It is, in general, too weak. An inequality is obtained which does express the principle.

Physical Review Letters•Feb 28, 1983•908 citations

On Covariance and Quantum Fisher Information

Shunlong Luo

For a quantum state and a set of observables, we can construct an associated covariance matrix and a natural quantum Fisher information matrix. These two matrices characterize the uncertainty and information content of the observables in the relevant state. An inequality between these two matrices is established. This inequality may be interpreted as a general quantification of the Heisenberg uncertainty principle from a statistical estimation perspective. In particular, it implies a new uncertainty relation which refines the celebrated Schrödinger uncertainty relation.

Theory of Probability and Its Applications•Jan 1, 2009•2 citations

Applications of a simple quantum mechanical formula

Lior Goldenberg, Lev Vaidman A

New applications of the formula A|ψ〉=〈A〉|ψ〉+ΔA|ψ⊥〉 are discussed. Simple derivations of the Heisenberg uncertainty principle and of related inequalities are presented. It is also shown that a state corresponding to a maximal uncertainty of any given observable cannot be unique.

American Journal of Physics•Aug 1, 1996•11 citations
Since the publication of Heisenberg’s paper1 on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality, ΔpΔq>h2π \Delta p\Delta q>\frac{h}{{2\pi}} ΔpΔq>2πh​ (1) This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.
The uncertainty principle, formulated by Heisenberg in 1927, is a fundamental principle in quantum mechanics. It forces us to review key concepts of classical physics, and from this analysis are born the concepts of quantum physics. Consequences of the Uncertainty principle also introduces the concept of incompatible sizes, a completely new concept compared to classical physics. A state of the system, which we call a quantum state, will be determined from the knowledge of a set maximum of certain quantities that are independent and compatible with each other. A measurable physical quantity is called an observable. If at a given moment a measurement is performed by one or more compatible observables it is said they are performing an observation of the system. The basic principles of quantum mechanics are expressed by a number of postulates. Their numbers and can vary from one text to another.
For a quantum state and a set of observables, we can construct an associated covariance matrix and a natural quantum Fisher information matrix. These two matrices characterize the uncertainty and information content of the observables in the relevant state. An inequality between these two matrices is established. This inequality may be interpreted as a general quantification of the Heisenberg uncertainty principle from a statistical estimation perspective. In particular, it implies a new uncertainty relation which refines the celebrated Schrödinger uncertainty relation.