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arXiv:1208.0034 · Physical Review Letters

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

Lee A. Rozema, Ardavan Darabi, Dylan H. Mahler, Alex Hayat, Yasaman Soudagar, Aephraim M. Steinberg

Published Sep 6, 2012• 308 citations

Abstract

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.

DOI: 10.1103/physrevlett.109.100404

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The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.

In this comment on the paper by F. Kaneda, S.-Y. Baek, M. Ozawa and K. Edamatsu [Phys. Rev. Lett. 112, 020402, 2014, arXiv:1308.5868], we point out that the claim of having refuted Heisenberg's error-disturbance relation is unfounded since it is based on the choice of unsuitable and operationally problematical quantifications of measurement error and disturbance. As we have shown elsewhere [PRL 111, 160405, 2013], for appropriate choices of operational measures of error and disturbance, Heisenberg's heuristic relation can be turned into a precise inequality which is a rigorous consequence of quantum mechanics.

Using formal definitions for the measurement precision and the disturbance (measurement back-action) η, Ozawa (2003 Phys. Rev. A 67 042105) has shown that Heisenberg's claimed relation between these quantities is false in general. Here, we show that the quantities introduced by Ozawa can be determined experimentally, using no prior knowledge of the measurement under investigation—both quantities correspond to the root-mean-squared difference given by a weak-valued probability distribution. We propose a simple three-qubit experiment that can illustrate the failure of Heisenberg's measurement–disturbance relation and the validity of an alternative relation proposed by Ozawa.

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