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:math-ph/0612074 · Journal of Mathematical Physics

Universal joint-measurement uncertainty relation for error bars

Paul Busch, David B. Pearson

Published Aug 1, 2007• 28 citations
arXivHTMLPDF

Abstract

We formulate and prove a new, universally valid uncertainty relation for the necessary error bar widths in any approximate joint measurement of position and momentum.
DOI
10.1063/1.2759831

Related papers

Error and unsharpness in approximate joint measurements of position and momentum

Paul Busch, David B. Pearson

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 form of a trade-off for the necessary errors in joint approximate measurements of position and momentum and other incompatible pairs of observables. Here we review some of these error measures, examine their properties and suitability, and compare their relative strengths as criteria for "good" approximations.

arXiv:1405.6956•May 27, 2014•2 citations

Uncertainty relations for realistic joint measurements of position and momentum in quantum optics

Ulf Leonhardt, B. Böhmer, Henryk Paul

Optics Communications•Sep 1, 1995•22 citations

An uncertainty relation for joint position-momentum measurements

Werner Stulpe, Stanley Gudder, James N. Hagler

Foundations of Physics Letters•Sep 1, 1988•8 citations

A universal formulation of uncertainty relation for errors

Jaeha Lee, Izumi Tsutsui

We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement of statistical nature. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable. Our relation violates the traditional naïve bound ħ / 2 for the position-momentum measurement while respecting Heisenberg's original philosophy of the uncertainty principle. Our relation entails, among others, the Arthurs–Kelly–Goodman and Ozawa relations as corollaries to its special cases, and also seamlessly reduces itself to the standard Kennard–Robertson (Schrödinger) relation when the measurement is non-informative.

Physics Letters A•Oct 5, 2024•3 citations

Uncertainty relations for joint localizability and joint measurability in finite-dimensional systems

Takayuki Miyadera

Two quantities quantifying uncertainty relations are examined. Busch and Pearson [J. Math. Phys. 48, 082103 (2007)] investigated the limitation on joint localizability and joint measurement of position and momentum by introducing overall width and error bar width. In this paper, we show a simple relationship between these quantities for finite-dimensional systems. Our result indicates that if there is a bound on joint localizability, it is possible to obtain a similar bound on joint measurability. For finite-dimensional systems, uncertainty relations for a pair of general projection-valued measures are obtained as by-products.

arXiv:1104.2096•Journal of Mathematical Physics•Jul 1, 2011•13 citations

Formulation of Uncertainty Relation Between Error and Disturbance in Quantum Measurement by Using Quantum Estimation Theory

Yu Watanabe

Springer theses•Dec 17, 2013•14 citations
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 form of a trade-off for the necessary errors in joint approximate measurements of position and momentum and other incompatible pairs of observables. Here we review some of these error measures, examine their properties and suitability, and compare their relative strengths as criteria for "good" approximations.
We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement of statistical nature. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable. Our relation violates the traditional naïve bound ħ / 2 for the position-momentum measurement while respecting Heisenberg's original philosophy of the uncertainty principle. Our relation entails, among others, the Arthurs–Kelly–Goodman and Ozawa relations as corollaries to its special cases, and also seamlessly reduces itself to the standard Kennard–Robertson (Schrödinger) relation when the measurement is non-informative.
Two quantities quantifying uncertainty relations are examined. Busch and Pearson [J. Math. Phys. 48, 082103 (2007)] investigated the limitation on joint localizability and joint measurement of position and momentum by introducing overall width and error bar width. In this paper, we show a simple relationship between these quantities for finite-dimensional systems. Our result indicates that if there is a bound on joint localizability, it is possible to obtain a similar bound on joint measurability. For finite-dimensional systems, uncertainty relations for a pair of general projection-valued measures are obtained as by-products.