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

arXiv:quant-ph/9707060 · Physical Review A

Strict bounds on the Franson inequality

Lev Vaidman A, Ori Belkind

Published Mar 1, 1998• 6 citations
arXivHTMLPDF

Abstract

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.
DOI
10.1103/physreva.57.1583

Related papers

Change and uncertainty in quantum systems

J. D. Franson

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.

Physical Review A•Nov 1, 1996•6 citations

Comment on “Uncertainty relations in terms of the Tsallis entropy”

Iwo Białynicki‐Birula, Łukasz Rudnicki

We prove that the inequality used recently by Wilk and W\l{}odarczyk [Phys. Rev. A 79, 062108 (2009)] to find a better lower bound in the uncertainty relations for the R\'enyi entropies is invalid. Thus, the problem of improving the bound given in our article [Phys. Rev. A 74, 052101 (2006)] remains unsolved.

arXiv:1001.4666•Physical Review A•Feb 9, 2010•11 citations

Sum uncertainty relations for arbitrary N incompatible observables

Bin Chen, Shao-Ming Fei

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 relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.

arXiv:1509.06931•Scientific Reports•Sep 15, 2015•74 citations

Strong unitary uncertainty relations

Bing Yu, Naihuan Jing, Xianqing Li‐Jost

In this paper we provide a set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are ``fine-grained'' compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in Phys. Rev. Lett. 120, 230402 (2018). to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims.

arXiv:1908.05053•Physical Review A•Aug 13, 2019•20 citations

Improved lower bounds for uncertaintylike relationships in many-body systems

Yan Alexander Wang, Emily A. Carter

We show that employing more stringent inequalities in the derivation of uncertaintylike relationships can improve their accuracy. In particular, Eq. (23) due to Romera et al. [Phys. Rev. A 59, 4064 (1999)] can be further improved using the Faris inequalities rather than using the H\"older inequalities.

Physical Review A•Nov 1, 1999•2 citations

Comment on “Geometric derivation of the quantum speed limit”

Marcin Zwierz

Recently, Jones and Kok [Jones and Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [Mandelstam and Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus-Levitin [Margolus and Levitin, Phys. D 120, 188 (1998)] inequalities for the quantum speed of dynamical evolution. The Margolus-Levitin inequality followed from an upper bound on the rate of change of the statistical distance between two arbitrary pure quantum states. We show that the derivation of this bound is incorrect. Subsequently, we provide two upper bounds on the rate of change of the statistical distance, expressed in terms of the standard deviation of the generator $K$ and its expectation value above the ground state. The bounds lead to the Mandelstam-Tamm inequality and a quantum speed limit which is only slightly weaker than the Margolus-Levitin inequality.

arXiv:1207.2208•Physical Review A•Jul 9, 2012•72 citations
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 relations are explicitly derived. These bounds are shown to be tighter than the ones such as derived from the uncertainty inequality for two observables [Phys. Rev. Lett. 113, 260401 (2014)]. Detailed examples are presented to compare among our results with some existing ones.
In this paper we provide a set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are ``fine-grained'' compared with the well-known Cauchy-Schwarz inequality, our framework naturally improves the results based on the latter. As such, the unitary uncertainty relations based on our method outperform the best known bound introduced in Phys. Rev. Lett. 120, 230402 (2018). to some extent. Explicit examples of unitary uncertainty relations are provided to back our claims.
Recently, Jones and Kok [Jones and Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [Mandelstam and Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus-Levitin [Margolus and Levitin, Phys. D 120, 188 (1998)] inequalities for the quantum speed of dynamical evolution. The Margolus-Levitin inequality followed from an upper bound on the rate of change of the statistical distance between two arbitrary pure quantum states. We show that the derivation of this bound is incorrect. Subsequently, we provide two upper bounds on the rate of change of the statistical distance, expressed in terms of the standard deviation of the generator KKK and its expectation value above the ground state. The bounds lead to the Mandelstam-Tamm inequality and a quantum speed limit which is only slightly weaker than the Margolus-Levitin inequality.