Letter | Published:

Experimental demonstration of a universally valid error–disturbance uncertainty relation in spin measurements

Nature Physics volume 8, pages 185189 (2012) | Download Citation

  • A Corrigendum to this article was published on 02 April 2012
  • A Corrigendum to this article was published on 01 August 2012

This article has been updated


The uncertainty principle generally prohibits simultaneous measurements of certain pairs of observables and forms the basis of indeterminacy in quantum mechanics1. Heisenberg’s original formulation, illustrated by the famous γ-ray microscope, sets a lower bound for the product of the measurement error and the disturbance2. Later, the uncertainty relation was reformulated in terms of standard deviations3,4,5, where the focus was exclusively on the indeterminacy of predictions, whereas the unavoidable recoil in measuring devices has been ignored6. A correct formulation of the error–disturbance uncertainty relation, taking recoil into account, is essential for a deeper understanding of the uncertainty principle, as Heisenberg’s original relation is valid only under specific circumstances7,8,9,10. A new error–disturbance relation, derived using the theory of general quantum measurements, has been claimed to be universally valid11,12,13,14. 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. The results confirm that both error and disturbance obey the new relation but violate the old one in a wide range of an experimental parameter.

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Change history

  • 12 March 2012

    In the version of this Letter originally published, in Fig. 5a a factor of /2 appeared incorrectly against the label 'Heisenberg lower limit' and in the figure caption. This error has been corrected in the HTML and PDF versions of the Letter.

  • 01 August 2012

    In the version of this Letter originally published, in the Methods section under the heading 'Error and disturbance in spin measurements: theoretical determination' the equation defining η(B) was incorrect — the term σϕ should have been divided by 2. This error has been corrected in the HTML and PDF versions of the Letter.


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We acknowledge support by the Austrian Science Fund (FWF), the European Research Council (ERC), the Japan Science and Technology Agency (JST) and The Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan. We thank H. Rauch, M. Arndt (Vienna) and A. Hosoya (Tokyo) for their helpful comments.

Author information


  1. Atominstitut, Vienna University of Technology, Stadionallee 2, 1020 Vienna, Austria

    • Jacqueline Erhart
    • , Stephan Sponar
    • , Georg Sulyok
    • , Gerald Badurek
    •  & Yuji Hasegawa
  2. Graduate School of Information Science, Nagoya University, Chikusa-ku, Nagoya 464-8601, Japan

    • Masanao Ozawa


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J.E., G.S. and S.S. carried out the experiment and analysed the data; G.B. contributed to the development at the early stage of the experiments; M.O. supplied the theoretical part and conceived the experiment; Y.H. conceived and carried out the experiment; all authors co-wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Yuji Hasegawa.

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