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External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications

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Quantum Foundations, Probability and Information

Abstract

In this critical essay, I present my personal reflections on QBism. I have no intrinsic sympathy neither to QBism nor to subjective interpretation of probability in general. However, I have been following the development of QBism from its very beginning, observing its evolution and success, sometimes with big surprise. Therefore my reflections on QBism can be treated as “external observer” reflections. I hope that my view on this interpretation of quantum mechanics (QM) has some degree of objectivity. It may be useful for researchers who are interested in quantum foundations, but do not belong to the QBism community, because I tried to analyze essentials of QBism critically (i.e., not just emphasizing its advantages, as in a typical QBist publication). QBists, too, may be interested in comments of an external observer who monitored development of this approach to QM during the last 16 years. (However, this paper cannot serve as an introduction to QBism. It neither concerns the philosophic issues around QBism.) Two sections are devoted to comparison of QBism with two interpretations of QM, the Växjö and information interpretations, which are close to QBism in two very different aspects, probabilistic and informational. The second part of the paper is devoted to interpretations of probability, objective versus subjective, and views of Kolmogorov, von Mises, and de Finetti. De Finetti’s approach to methodology of science is presented and compared with QBism. One of the outputs of this comparison is understanding of restrictiveness of QBism, where the subjective probability viewpoint is applied only to QM. One of the main messages of this paper is that QBism has to be completed by CBism (classical physics Bayesianism). Finally, the possibility to use QBism as the general interpretational basis for applications of the quantum probabilistic formalism for decision-making outside of physics (in cognitive, social, and political sciences, psychology, economics, finances) is considered.

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Notes

  1. 1.

    The discussion is definitely not systematic enough to serve as an introduction to QBism. If the reader seeks a scholarly discussion, a good starting point would be the fairly recent books of Friederich [25] and Timpson [80], for example (see also their papers [24, 79]). Readers who are already conversant with QBism are unlikely to find anything new in our presentation. These notes have two closely related aims: (a) to add some details to the history of foundation and evolution of QBism and (b) to send a message to the part of physical community which still strongly rejects QBism as a totally unphysical interpretation of QM. It is important that these notes were written by one of the active representatives of this anti-QBist lobby which still strongly dominates in quantum foundations. I definitely have not been completely converted into QBism, but recently I started to find rational points in QBist views on quantum theory, and I want to present these points, but, so to say, with a spicy sauce of doubt.

  2. 2.

    From this viewpoint, i.e., QM as a probability update machine, QBism is similar to the Växjö interpretation of QM. The latter is a realist contextual statistical interpretation, so ideologically it is opposite to QBism. However, the probability update basis makes it close to QBism. At the same time, even this closeness is only formal, since the QBism version of generalized FTP differs crucially from the Växjö version.

  3. 3.

    Besides QBism, we can mention the Växjö interpretation of QM (statistical realist and contextual) [45, 46] derivation of the QM-formalism from simple operational principles, D’ Ariano [17, 18] and Chiribella et al. [15, 16] (first time this project was also announced in Växjö), and the statistical Copenhagen interpretation (statistical non-realist) which final formulation was presented at the Växjö-15 conference by A. Plotnitsky and based on his previous studies about the probabilistic structure of QM [67,68,69,70].

  4. 4.

    Gnedenko was the author of one of the best textbooks on probability theory [36]. The introduction of this book contains the manifesto of objective probability and sharp critique of subjective probability.

  5. 5.

    Once Christopher Fuchs asked me: “Why did you support QBism so strongly during the Växjö-series of conferences? QBism contradicts your own Växjö interpretation!” In fact, I was not able to explain this even for myself. I had a feeling that QBIsm can be useful. But how? and where?

  6. 6.

    In the mentioned debates, I also was strongly against the anti-realist attitude of QBism. However, now this attitude does not disturb me so much as 12 years ago. Either I started to understand QBists’ views on the problem of realism better or QBists changed their views (or both). QBism needs not appeal to any subquantum model providing the ontic description of quantum systems and processes, in particular, to hidden variables. Nor is QBism concerned with struggle against such models. It seems that the personal position of C. Fuchs is similar to the position of N. Bohr [4,5,6]: for quantum physics, it plays no role whether finally one would be able to construct a realistic subquantum model or not. For the present state of development of quantum theory, this is the most reasonable position, cf. with Zeilinger’s strong anti-realist attitude. Moreover, just recently (through a series of email exchanges), I understood better the position of C. Fuchs on the problem of non-realism/realism. Surprisingly QBists (at least C. Fuchs) do not consider QBism as a non-realist interpretation of QM.

  7. 7.

    We remark that in coming considerations, the interpretation of probabilities does not play any role. They can be subjective probabilities (as originally in QBism), but they also can be statistical, e.g., Kolmogorovian or Misesian, as well.

  8. 8.

    As was remarked, probability can be interpreted in other ways. The situation is similar to the classical probability update. De Finetti would treat this probability as subjective but Kolmogorov, or Gnedenko, or von Mises as statistical.

  9. 9.

    However, for QBists the above generalization—to start the probability update scheme with an arbitrary POVM measurement G = (G j ) and not with a SIC-POVM E = (E i )—seems to be unacceptable. They are really addicted on SIC-POVMs and on completeness of information gained at the first step, information about the state, even at the price of appearance of counterfactuals.

  10. 10.

    This is a contextual realistic interpretation of QM. Contextuality is understood in the wider sense than typically in modern discussions on Bell’s inequality in which contextuality is reduced to joint measurement with another observable. In the Växjö interpretation, contextuality is understood in the spirit of Bohr [4,5,6]: as dependence of the outcomes of observables on the whole experimental arrangement. In particular, violation of Bell’s inequality is a consequence of complementarity of experimental contexts corresponding to different pairs of orientations of polarization beam splitters. In some sense the Växjö interpretation is an attempt to unify the views of Einstein and Bohr. This interpretation matches with the statistical interpretation of probability. In works [42, 47] the frequency (von Mises [81,82,83]) approach to the notion of probability was explored. We remark that both Einstein and Bohr shared the statistical viewpoint on probability; see [71] for the corresponding discussion.

  11. 11.

    The strong anti-Copenhagen attitude in the first declaration about the Växjö interpretation was partially a consequence of the active advertising of QBism at Växjö-2001 conference. My reaction (as many others) was: “See, the Copenhagen interpretation finally led to such a perverse view on QM as the private agent’s perspective on the quantum state.”

  12. 12.

    Here the symbol σ encodes “countable.” In American terminology, such systems of subsets are called σ-fields.

  13. 13.

    Here measurability has the following meaning. The set of real numbers R is endowed with the Borel σ-algebra \(\mathcal {B}:\) the minimal σ-algebra containing all open and closed intervals. Then for any \(A\in \mathcal {B}\) its inverse image \(a^{-1}(A) \in \mathcal {F}.\) This gives a possibility to define on \(\mathcal {B}\) the probability distribution of a random variable, p a (A) = p(a −1(A)).

  14. 14.

    By this principle the probability of some concrete output α of measurement is defined as the limit of the relative frequency of realizations of α in a long (in fact, infinitely long) sequence of trials. The class of sequences of trials which can serve to determine probabilities is constrained by another fundamental principle of von Mises’ theory—the principle of randomness. Sequences of trials satisfying the latter are called collectives (random sequences). The principle of randomness involves the ambiguous notion of a place selection. On one hand, the ambiguity of this notion was the main pitfall for applications of von Mises’ frequency theory of probability. And nowadays it is practically forgotten. On the other hand, this ambiguity (as often happens in science) played the crucial role in establishing of modern theory of randomness and algorithms.

  15. 15.

    It is a good place to point out that these paradoxes cannot be solved simply by playing with the interpretations of probability. The essence of the problem is not an interpretation but the structure of the probability calculus. Thus by using QBism to resolve these paradoxes we use both its fundamental counterparts, interpretational—the subjective interpretation of probability, and mathematical—the Born rule.

  16. 16.

    According to Derrida, “what we get when we read a text is not an objective account of logos or even what the author really meant, but our present interpretation or understanding of the text itself. This understanding becomes so to speak, our own [text] of the text” (quoted from [66, p. 368]).

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    Andrei Khrennikov

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    Bourama Toni

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Khrennikov, A. (2018). External Observer Reflections on QBism, Its Possible Modifications, and Novel Applications. In: Khrennikov, A., Toni, B. (eds) Quantum Foundations, Probability and Information. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-319-74971-6_9

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