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

Position-Measurement Errors in the Heisenberg Uncertainty Principle

誠司 小杉, Seiji Kosugi

Published Feb 25, 2009• 0 citations
OpenAlex

Abstract

測定過程に関連したHeisenbergの不確定性原理に対する小澤の批判を考察し,小澤が定義した測定値が正しくないために,小澤の理論にはいくつかの不合理な点が存在することを指摘した.本論文で明らかにした正しい測定値を用いれば,これらの問題は生じない.EPRがおこなった粒子2の位置測定の結果から粒子1の位置測定をおこなう間接測定の場合には,Heisenbergの不確定性関係を一般化した小澤の不等式は成立していない.

Related papers

Position measuring interactions and the Heisenberg uncertainty principle

Masanao Ozawa

arXiv:quant-ph/0107001•Physics Letters A•Jun 1, 2002•38 citations

Uncertainty in the Results of Position Measurement in the Heisenberg Uncertainty Principle

Seiji Kosugi

Heisenbergの不確定性原理において,位置の測定値の不確定性として何を用いるべきかについて考察した.測定対象の位置としては,測定前の位置x0と測定後の位置xtの2つが考えられる.位置xtの測定値(xt)expの不確定性はこの測定値の測定誤差ε(xt)である.しかし位置x0の測定値(x0)expの不確定性は測定誤差ε(x0)ではなく,測定値(x0)expの標準偏差σ((x0)exp)である.位置の測定値の不確定性としてε(xt)またはσ((x0)exp)を用いた場合には,Heisenbergの不確定性関係は成立している.2つの位置情報の不確定性ε(xt)とσ((x0)exp)の非対称性を引き起こしているのは波束の収縮である.

•Feb 25, 2011•0 citations

Error-disturbance uncertainty relations in neutron spin measurements

Stephan Sponar

Heisenberg’s uncertainty principle in a formulation of uncertainties, intrinsic to any quantum system, is rigorously proven and demonstrated in various quantum systems. Nevertheless, Heisenberg’s original formulation of the uncertainty principle was given in terms of a reciprocal relation between the error of a position measurement and the thereby induced disturbance on a subsequent momentum measurement. However, a naive generalization of a Heisenberg-type error-disturbance relation for arbitrary observables is not valid. An alternative universally valid relation was derived by Ozawa in 2003. Though universally valid, Ozawa’s relation is not optimal. Recently, Branciard has derived a tight error-disturbance uncertainty relation (EDUR), describing the optimal trade-off between error and disturbance under certain conditions. Here, we report a neutron-optical experiment that records the error of a spin-component measurement, as well as the disturbance caused on another spin-component to test EDURs. We demonstrate that Heisenberg’s original EDUR is violated, and Ozawa’s and Branciard’s EDURs are valid in a wide range of experimental parameters, as well as the tightness of Branciard’s relation.

International Journal of Quantum Information•May 21, 2016•0 citations

Experimental test of the Heisenberg uncertainty relation for position and momentum

Winfrid Görlich, Ingo Hoffmann, Thomas Schürmann

•Dec 27, 2008•0 citations

Proof of Heisenberg's error-disturbance principle

Seiji Kosugi

In Heisenberg's error-disturbance relation for electron position measurement, the measurement error must be the one that determines the uncertainty in the electron position just after the measurement. It is the resolution $ε(x_t)$ i.e., the measurement error of the post-measurement observable $\hat{x}_t$, not the precision $ε(x_0)$ i.e., that of the pre-measurement observable $\hat{x}_0$ that determines the uncertainty of the observable $\hat{x}_t$. Therefore, Heisenberg's relation must be interpreted as one between the resolution $ε(x_t)$ and the disturbance $η(y_0)$. The magnitude of the disturbance $η(y_0)$ is independent of the definition of the measurement value of the observable $\hat{x}_t$. Heisenberg's error-disturbance relation is proven to hold true in general, when the measurement value of $\hat{x}_t$ is defined in order to minimize the resolution $ε(x_t)$.

arXiv:1504.03779•Apr 15, 2015•0 citations

The uncertainty principle and measurement accuracy

Aleksandr V. Belinsky, V. B. Lapshin

Abstract A gedanken experiment is proposed in which the momentum and position of a photon can be measured simultaneously in such a way that the product of their respective errors is less than the right-hand side of the appropriate Heisenberg uncertainty relation.

Physics-Uspekhi•Mar 3, 2017•6 citations
測定過程に関連したHeisenbergの不確定性原理に対する小澤の批判を考察し,小澤が定義した測定値が正しくないために,小澤の理論にはいくつかの不合理な点が存在することを指摘した.本論文で明らかにした正しい測定値を用いれば,これらの問題は生じない.EPRがおこなった粒子2の位置測定の結果から粒子1の位置測定をおこなう間接測定の場合には,Heisenbergの不確定性関係を一般化した小澤の不等式は成立していない.
Heisenbergの不確定性原理において,位置の測定値の不確定性として何を用いるべきかについて考察した.測定対象の位置としては,測定前の位置x0と測定後の位置xtの2つが考えられる.位置xtの測定値(xt)expの不確定性はこの測定値の測定誤差ε(xt)である.しかし位置x0の測定値(x0)expの不確定性は測定誤差ε(x0)ではなく,測定値(x0)expの標準偏差σ((x0)exp)である.位置の測定値の不確定性としてε(xt)またはσ((x0)exp)を用いた場合には,Heisenbergの不確定性関係は成立している.2つの位置情報の不確定性ε(xt)とσ((x0)exp)の非対称性を引き起こしているのは波束の収縮である.
Heisenberg’s uncertainty principle in a formulation of uncertainties, intrinsic to any quantum system, is rigorously proven and demonstrated in various quantum systems. Nevertheless, Heisenberg’s original formulation of the uncertainty principle was given in terms of a reciprocal relation between the error of a position measurement and the thereby induced disturbance on a subsequent momentum measurement. However, a naive generalization of a Heisenberg-type error-disturbance relation for arbitrary observables is not valid. An alternative universally valid relation was derived by Ozawa in 2003. Though universally valid, Ozawa’s relation is not optimal. Recently, Branciard has derived a tight error-disturbance uncertainty relation (EDUR), describing the optimal trade-off between error and disturbance under certain conditions. Here, we report a neutron-optical experiment that records the error of a spin-component measurement, as well as the disturbance caused on another spin-component to test EDURs. We demonstrate that Heisenberg’s original EDUR is violated, and Ozawa’s and Branciard’s EDURs are valid in a wide range of experimental parameters, as well as the tightness of Branciard’s relation.
In Heisenberg's error-disturbance relation for electron position measurement, the measurement error must be the one that determines the uncertainty in the electron position just after the measurement. It is the resolution ε(xt)ε(x_t)ε(xt​) i.e., the measurement error of the post-measurement observable x^t\hat{x}_tx^t​, not the precision ε(x0)ε(x_0)ε(x0​) i.e., that of the pre-measurement observable x^0\hat{x}_0x^0​ that determines the uncertainty of the observable x^t\hat{x}_tx^t​. Therefore, Heisenberg's relation must be interpreted as one between the resolution ε(xt)ε(x_t)ε(xt​) and the disturbance η(y0)η(y_0)η(y0​). The magnitude of the disturbance η(y0)η(y_0)η(y0​) is independent of the definition of the measurement value of the observable x^t\hat{x}_tx^t​. Heisenberg's error-disturbance relation is proven to hold true in general, when the measurement value of x^t\hat{x}_tx^t​ is defined in order to minimize the resolution ε(xt)ε(x_t)ε(xt​).