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 $ε(x_t)$ .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:1504.03779Apr 15, 20150 citations

Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler +3 more

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's uncertainty principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's uncertainty principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.

arXiv:1208.0034Physical Review LettersSep 6, 2012308 citations

The Uncertainty Principle of Heisenberg

John Stringer

Elsevier eBooksJan 1, 19670 citations

Heisenberg uncertainty for qubit measurements

Paul Busch, PEKKA J. LAHTI, Reinhard F. Werner

Reports on experiments recently performed in Vienna [Erhard et al., Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of $\ifmmode\pm\else\textpm\fi{}1$-valued observables $A,B$ are tightly bounded from below by a quantity that measures the degree of incompatibility of $A$ and $B$ . The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.Reports on experiments recently performed in Vienna [Erhard et al., Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of $\ifmmode\pm\else\textpm\fi{}1$-valued observables $A,B$ are tightly bounded from below by a quantity that measures the degree of incompatibility of $A$ and $B$. The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.

arXiv:1311.0837Physical Review AJan 31, 2014119 citations

Heisenberg Uncertainty Principle

WORLD SCIENTIFIC eBooksOct 26, 20260 citations

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)

A,B

are tightly bounded from below by a quantity that measures the degree of incompatibility of

A

and

B

. The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.