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

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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Fig. 1

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.

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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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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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Keywords

  • QBism
  • Wigner's friend
  • Response to Frauchiger and Renner thought experiment