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arXiv:1201.5151

Comment on "Experimental demonstration of a universally valid error-disturbance uncertainty relation in spin measurements"

Y. Kurihara

Published Jan 24, 2012• 1 citation
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Abstract

In this comment we show that the experimental results for a universally valid uncertainty relation in ref.[J. Erhart et al. Nat. Phys.(2012)10.1038/nphys2194]cannot be justified. The experiments cannot be recognized to establish a violation of the Heisenberg-type uncertainty relation suggested by Ozawa[Phys. Lett. A318(2003)21, Phys. Rev. A67(2003)042105].

DOI
10.48550/arxiv.1201.5151

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In this comment we show that the experimental results for a universally valid uncertainty relation in ref.[J. Erhart et al. Nat. Phys.(2012)10.1038/nphys2194]cannot be justified. The experiments cannot be recognized to establish a violation of the Heisenberg-type uncertainty relation suggested by Ozawa[Phys. Lett. A318(2003)21, Phys. Rev. A67(2003)042105].
A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart et al. [Nat. Phys. 8, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs–Kelly uncertainty relation, which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs–Kelly uncertainty relation and the Heisenberg error–disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation, as is widely accepted.
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.
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 its original formulation, Heisenberg's uncertainty principle dealt with the relationship between the error of a quantum measurement and the thereby induced disturbance on the measured object. Meanwhile, Heisenberg's heuristic arguments have turned out to be correct only for special cases. An alternative universally valid relation was derived by Ozawa in 2003. Here, we demonstrate that Ozawa's predictions hold for projective neutron-spin measurements. The experimental inaccessibility of error and disturbance claimed elsewhere has been overcome using a tomographic method. By a systematic variation of experimental parameters in the entire configuration space, the physical behavior of error and disturbance for projective spin-12\frac{1}{2}21​ measurements is illustrated comprehensively. The violation of Heisenberg's original relation, as well as the validity of Ozawa's relation become manifest. In addition, our results conclude that the widespread assumption of a reciprocal relation between error and disturbance is not valid in general.