- Physical Review Journals
All JournalsPhysics Magazine

APS Open Science

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Inaccurate weak measurements classical and quantum

D. Sokolovski1,2,3,*, D. Alonso4, and S. Brouard4

  • *Contact author: dgsokol15@gmail.com
PDF

APS Open Sci. 1, 000102 – Published 24 August, 2026

DOI: https://doi.org/10.1103/t6gz-b6vt

Abstract

We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case, such a “weak” measurement preserves coherence between the system's alternatives. We demonstrate that in both classically and quantally the information about the scenario realized in each individual trial is lost. However, ensemble parameters such as classical path probabilities and quantum quasiprobabilities can be extracted from the obtained statistics. Both classically and quantally, causality ensures that additional postselection only redistributes individual outcomes between the system's final states. Quantum quasiprobabilities may change sign, which allows for anomalously large meter's (pointer's) reading for some final states. These, we show, result from mere “reshaping” of a broad distribution obtained earlier and provide no “experimental evidence” of quantum variables taking, albeit on rare occasions, exceptionally large or otherwise anomalous values.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (29)

  1. Y. Aharonov, D. Z. Albert, and L. Vaidman, How the result of a measurement of a component of a spin-1/2 particle can turn out to be 100, Phys. Rev. Lett. 60, 1351 (1988).
  2. R. P. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics III (Dover Publications, New York, 1989).
  3. D. Bohm, Quantum Theory (Dover Publications, NY, 1989), p. 600.
  4. R. P. Feynman, The Character of Physical Law (MIT Press, London, 1985).
  5. Y. Aharonov and L. Vaidman, Complete description of a quantum system at a given time, J. Phys. A: Math. Gen. 24, 2315 (1991).
  6. Y. Aharonov, S. Popescu, and J. Tollaksen, A time-symmetric formulation of quantum mechanics, Phys. Today 63(11) (2010).
  7. K. Robertson, Can the two-time interpretation of quantum mechanics solve the measurement problem? Stud. Hist. Philos. Sci. Part B: Stud. Hist. Philos. Mod. Phys. 58, 54 (2017).
  8. J. A. Barandes, The trouble with weak values, arXiv:2602.09380.
  9. D. Sokolovski, D. A. Ramirez, and S. B. Martin, Speakable and unspeakable in quantum measurements, Ann. Phys. 535, 2300261 (2023).
  10. J. Dressel, M. Malik, F. M. Miatto, N. Jordan, and R. W. Boyd, Colloquium: Understanding quantum weak values: Basics and applications, Rev. Mod. Phys. 86, 307 (2014).
  11. D. Sokolovski, Weak measurements measure probability amplitudes (and very little else), Phys. Lett. A 380, 1593 (2016).
  12. C. Ferry and J. Combes, How the result of a single coin toss can turn out to be 100 heads, Phys. Rev. Lett. 113, 120404 (2014).
  13. A. Brodutch, Comment on “How the result of a single coin toss can turn out to be 100 heads”, Phys. Rev. Lett. 114, 118901 (2015).
  14. A. Uranga, E. Akhmatskaya, and D. Sokolovski, Quantum weak values and the question, Entropy 27, 259 (2025).
  15. A. Peres, Quantum measurements with postselection, Phys. Rev. Lett. 62, 2326 (1989).
  16. E. C. Zeeman, Catastrophe Theory: Selected Papers (Addison-Wesley Educational Publishers, Inc., Boston, MA, 1977).
  17. S. N. Sahoo, S. Chakraborti, S. Kanjilal, S. R. Behera, D. Home, A. Matzkin, and U. Sinha, Unambiguous joint detection of spatially separated properties of a single photon in the two arms of an interferometer, Commun. Phys. 6, 203 (2023).
  18. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955), Chap. VI, pp. 183–217.
  19. E. Wigner, On the quantum correction for thermodynamic equilibrium, Phys. Rev. 40, 749 (1932).
  20. R. P. Feynman, Negative probability, in Quantum Implications: Essays in Honour of David Bohm, edited by F. D. Peat and B. Hiley (Routledge & Kegan Paul Ltd., London, 1987), p. 235.
  21. M. S. Bartlett, Negative probability, Math. Proc. Cambridge Philos. Soc. 41, 71 (1945).
  22. B. L. Higgins, M. S. Palsson, G. Y. Xiang, H. M. Wiseman, and G. J. Pryde, Using weak values to experimentally determine in a two-photon state with Bell correlations, Phys. Rev. A 91, 012113 (2015).
  23. J. Ryu, S. Hong, J.-S. Lee, K. H. Seol, J. Jae, J. Lim, J. Lee, K.-G. Lee, and J. Lee, Optical experiment to test negative probability in context of quantum measurement selection, Sci. Rep. 9, 19021 (2019).
  24. R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
  25. Or just take a pair of scissors and cut along the dashed line in Fig. 4.
  26. R. S. Dumont, T. Rivlin, and E. Pollak, The relativistic tunneling flight time may be superluminal, but it does not imply superluminal signaling, New J. Phys. 22, 093060 (2020).
  27. M. Yu, K. Liu, M. Li, J. Yan, C. Cao, J. Tan, J. Liang, K. Guo, W. Cao, P. Lan, et al., Full experimental determination of tunneling time with attosecond-scale streaking method, Light: Sci. Appl. 11, 215 (2022).
  28. D. Sokolovski and E. Akhmatskaya, Superluminal paradox' in wave packet propagation and its quantum mechanical resolution, Ann, Phys. 339, 307 (2013).
  29. D. Sokolovski and E. Akhmatskaya, No time at the end of the tunnel, Commun. Phys. 1, 47 (2018).

Outline

Information

APS Open Sci. 1, 000102– Published 24 August, 2026
Vol. 1
  • Received 30 March 2026
  • Revised 9 July 2026
  • Accepted 12 August 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation