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Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend

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Abstract

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner’s conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner’s original thought experiment was central to the development of QBist thinking. The focus of this paper concerns two very instructive modifications to Wigner’s puzzle: One, a recent no-go theorem by Frauchiger and Renner (Nat Commun 9:3711, 2018), and the other a thought experiment by Baumann and Brukner (Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky, Springer, Cham, 2020). We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner’s action on his friend then becomes, from the friend’s perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner’s original paper, neither agent should be considered as in “suspended animation.” In this light, QBism brings an entirely new perspective to understanding Wigner’s friend thought experiments.

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Notes

  1. There are too many responses to these papers to cite here, but a sampling of those which attempt to analyse QBism’s relation to the thought experiments can be found in Refs. [12,13,14,15,16,17,18,19,20]. Though Refs. [19, 20] are both very relevant to QBist interests, neither of these get at the heart of the argument made here.

  2. It is easier to see how \(p_j\), \(\rho\), and \(E_j\) are on an equal footing if \(\rho\) and \(E_j\) are expressed as probabilities. That this can be done is well known: with respect to an appropriately chosen informationally complete measurement, any density operator is equivalent to a vector of probabilities [37], and any POVM \(\{E_1,\ldots ,E_n\}\) is characterized by a stochastic matrix of conditional probabilities [5].

  3. Baumann and Brukner assume the experiment is repeated many times, so that the alleged contradiction can be phrased in frequentist terms. From a QBist perspective, the full force of the contradiction arises already in the single-case analysis given here.

References

  1. Frauchiger, D., Renner, R.: Quantum theory cannot consistently describe the use of itself. Nat. Commun. 9, 3711 (2018)

    Article  ADS  Google Scholar 

  2. Baumann, V., Brukner, Č.: Wigner’s friend as a rational agent. In: M. Hemmo and O. Shenker (eds.) Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky, pp. 91–99. Springer, Cham (2020)

    Chapter  Google Scholar 

  3. Wigner, E.P.: Remarks on the mind-body question. In: I.J. Good (William Heinemann Ltd, London, 1961), pp. 284–302 reprinted in E.P. Wigner, Symmetries and Reflections: Scientific Essays of Eugene Wigner, (ed.) The Scientist Speculates, pp. 171–184. Ox Bow Press, Woodbridge (1979)

  4. Fuchs, C.A.: QBism, the perimeter of quantum Bayesianism, arXiv:1003.5209

  5. Fuchs, C.A., Schack, R.: Quantum-Bayesian coherence. Rev. Mod. Phys. 85, 1693–1715 (2013)

    Article  ADS  Google Scholar 

  6. Fuchs, C.A., Mermin, N.D., Schack, R.: An introduction to QBism with an application to the locality of quantum mechanics. Am. J. Phys. 82, 749–754 (2014)

    Article  ADS  Google Scholar 

  7. Caves, C.M., Fuchs, C.A., Schack, R.: Subjective probability and quantum certainty. Stud. Hist. Phil. Mod. Phys. 38, 255–274 (2007)

    Article  MathSciNet  Google Scholar 

  8. Pusey, M.F.: An inconsistent friend. Nat. Phys. 14(10), 977–978 (2018)

    Article  Google Scholar 

  9. Fuchs, C.A.: My Struggles with the Block Universe: Selected Correspondence, January 2001–May 2011. In: Stacey, B.C. foreword by Maximilian Schlosshauer, p. 2349 (2014). arXiv:1405.2390

  10. Brukner, Č.: On the quantum measurement problem. In: Bertlmann, R., A. Zeilinger, A. (eds.) Quantum [Un]Speakables II: Half a Century of Bell’s Theorem, pp. 95–118. Springer, Berlin (2017). arXiv:1507.05255. First presented at Quantum Physics of Nature (QUPON), Vienna, Austria, 22 May 2015

  11. Brukner, Č.: A no-go theorem for observer-independent facts. Entropy 20, 350 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  12. Healey, R.: Quantum theory and the limits of objectivity. Found. Phys. 48, 1568–1589 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  13. Nurgalieva, N., del Rio, L.: Inadequacy of modal logic in quantum settings, arXiv:1804.01106

  14. Proietti, M., Pickston, A., Graffitti, F., Barrow, P., Kundys, D., Branciard, C., Ringbauer, M., Fedrizzi, A.: Experimental test of local observer independence. Sci. Adv. 5, eaaw9832 (2019)

    Article  ADS  Google Scholar 

  15. Krismer, R.: Representation lost: the case for a relational interpretation of quantum mechanics. Entropy 20, 975 (2019)

    Article  ADS  Google Scholar 

  16. Boge, F.: Quantum information versus epistemic logic: an analysis of the Frauchiger-Renner theorem. Found. Phys. 49, 1143–1165 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  17. Sudbery, A.: The hidden assumptions of Frauchiger and Renner, arXiv:1905.13248

  18. Evans, P.W.: Perspectival objectivity or: how I learned to stop worrying and love observer-dependent reality, (2019), https://philsci-archive.pitt.edu/16956/  

  19. Suarez, A.: The limits of quantum superposition: should ‘Schrödinger’s cat’ and ‘Wigner’s friend’ be considered ‘miracle’ narratives?, arXiv:1906.10524

  20. Stacey, B.C.: On QBism and Assumption (Q), arXiv:1907.03805

  21. Fuchs, C.A., Stacey, B C.: QBism: quantum theory as a hero’s handbook. In: Rasel, E.M., Schleich, W.P., Wölk, S. (eds.) Proceedings of the International School of Physics “Enrico Fermi” Course 197—Foundations of Quantum Physics, pp. 133–202. IOS Press, Amsterdam; Società Italiana di Fisica, Bologna, (2018), arXiv:1612.07308

  22. Fuchs, C.A.: Notwithstanding Bohr, the reasons for QBism. Mind Matter 15, 245–300 (2017)

    Google Scholar 

  23. Stacey, B.C.: Ideas abandoned en route to QBism, arXiv:1911.07386

  24. Khrennikov, A.: Quantum Bayesianism as the basis of general theory of decision-making. Philos. Trans. A 374, 2068 (2016)

    MathSciNet  MATH  Google Scholar 

  25. Khrennikov, A.: Towards better understanding QBism. Found. Sci. 23, 181–195 (2018)

    Article  MathSciNet  Google Scholar 

  26. Müller, T., Briegel, H.J.: A stochastic process model for free agency under indeterminism. Dialectica 72, 219–252 (2018)

    Article  MathSciNet  Google Scholar 

  27. Briegel, H.J.: On creative machines and the physical origins of freedom. Sci. Rep. 2, 522 (2012)

    Article  ADS  Google Scholar 

  28. DeBrota, J.B., Stacey, B.C.: FAQBism, arXiv:1810.13401

  29. Timpson, C.G.: Quantum Bayesianism: A study. Stud. Hist. Philos. Mod. Phys. 39, 579–609 (2008)

    Article  MathSciNet  Google Scholar 

  30. Mermin, N.D.: Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it. In: Bertlmann, R., Zeilinger, A. (eds.) Quantum [Un]Speakables II: Half a Century of Bell’s Theorem, pp. 83–94. Springer, Berlin (2017)

    Chapter  Google Scholar 

  31. Fuchs, C.A.: On participatory realism. In: Durham, I.T., Rickles, D. (eds.) Information and Interaction: Eddington, Wheeler, and the Limits of Knowledge, pp. 113–134. Springer, Berlin (2016)

    Google Scholar 

  32. Healey, R.: Quantum-Bayesian and pragmatist views of quantum theory. Stanford Encylopedia Philos. (2016)

  33. Savage, L.J.: The Foundations of Statistics, 2nd edn. Dover, New York (1972)

    MATH  Google Scholar 

  34. Bernardo, J.M., Smith, A.F.M.: Bayesian Theory. Wiley, Chichester (1994)

    Book  Google Scholar 

  35. de Finetti, B.: Theory of Probability. Wiley, New York (1990)

    MATH  Google Scholar 

  36. Berkovitz, J.: On de Finetti’s instrumentalist philosophy of probability. Euro. J. Philos. Sci. 9, 25 (2019)

    Article  MathSciNet  Google Scholar 

  37. Caves, C.M., Fuchs, C.A., Schack, R.: Unknown quantum states: the quantum de Finetti representation. J. Math. Phys. 43, 4537 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  38. Wallace, D.: A Case for QBism, Presentation at the XII International Ontology Congress, San Sebastian, Spain, 5 October 2016

  39. Fuchs, C.A.: Quantum Mechanics as Quantum Information (and only a little more), arXiv:quant-ph/0205039

  40. Peres, A.: Unperformed experiments have no results. Am. J. Phys. 46, 745–747 (1978)

    Article  ADS  Google Scholar 

  41. Feynman, R.P.: The concept of probability in quantum mechanics. In: Neyman, J. (ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 533–541. University of California Press, Berkeley (1951)

    Google Scholar 

  42. Pusey, M.F., Barrett, J., Rudolph, T.: On the reality of the quantum state. Nat. Phys. 8, 475–478 (2012)

    Article  Google Scholar 

  43. Colbeck, R., Renner, R.: Is a system’s wave function in one-to-one correspondence with its elements of reality? Phys. Rev. Lett. 108, 150402 (2012)

    Article  ADS  Google Scholar 

  44. Deutsch, D.: Quantum theory as a universal physical theory. Int. J. Theoret. Phys. 24, 1–41 (1985)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

We would like to thank Renato Renner, Časlav Brukner, Veronika Baumann, and Jacques Pienaar for many valuable discussions. CAF was supported in part by the John E. Fetzer Memorial Trust; CAF and JBD were further supported by grant FQXi-RFP-1811B of the Foundational Questions Institute.

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Authors and Affiliations

  1. Department of Physics, University of Massachusetts Boston, 100 Morrissey Boulevard, Boston, MA, 02125, USA

    John B. DeBrota & Christopher A. Fuchs

  2. Department of Mathematics, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    Rüdiger Schack

  3. Stellenbosch Institute for Advanced Study (STIAS), Wallenberg Research Centre, Marais Street, Stellenbosch, 7600, South Africa

    John B. DeBrota, Christopher A. Fuchs & Rüdiger Schack

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  1. John B. DeBrota
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Correspondence to Christopher A. Fuchs.

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DeBrota, J.B., Fuchs, C.A. & Schack, R. Respecting One’s Fellow: QBism’s Analysis of Wigner’s Friend. Found Phys 50, 1859–1874 (2020). https://doi.org/10.1007/s10701-020-00369-x

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