A “thoughtful” Local Friendliness no-go theorem: a prospective experiment with new assumptions to suit

Howard M. Wiseman1,2, Eric G. Cavalcanti3, and Eleanor G. Rieffel4

1Centre for Quantum Computation and Communication Technology (Australian Research Council)
2Centre for Quantum Dynamics, Griffith University, Yuggera Country, Brisbane, Queensland 4111, Australia
3Centre for Quantum Dynamics, Griffith University, Yugambeh Country, Gold Coast, Queensland 4222, Australia
4QuAIL (Quantum Artifical Intelligence Laboratory), NASA Ames Research Center, Moffett Field, CA 94035, United States of America

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A recent paper by two of us and co-workers [1], based on an extended Wigner's friend scenario, demonstrated that certain empirical correlations predicted by quantum theory (QT) violate inequalities derived from a set of metaphysical assumptions we called "Local Friendliness" (LF). These assumptions are strictly weaker than those used for deriving Bell inequalities. Crucial to the theorem was the premise that a quantum system with reversible evolution could be an observer (colloquially, a "friend"). However, that paper was noncommittal on what would constitute an observer for the purpose of an experiment. Here, we present a new LF no-go theorem which takes seriously the idea that a system's having $thoughts$ is a sufficient condition for it to be an observer. Our new derivation of the LF inequalities uses four metaphysical assumptions, three of which are thought-related, including one that is explicitly called "Friendliness". These four assumptions, in conjunction, allow one to derive LF inequalities for experiments involving the type of system that "Friendliness" refers to. In addition to these four metaphysical assumptions, this new no-go theorem requires two assumptions about what is $technologically$ feasible: Human-Level Artificial Intelligence, and Universal Quantum Computing which is fast and large scale. The latter is often motivated by the belief that QT is universal, but this is $not$ an assumption of the theorem. The intent of the new theorem is to give a clear goal for future experimentalists, and a clear motivation for trying to achieve that goal. We review various approaches to QT in light of our theorem. The popular stance that "quantum theory needs no interpretation" does not question any of our assumptions and so is ruled out. Finally, we quantitatively discuss how difficult the experiment we envisage would be, and briefly discuss milestones on the paths towards it.

In recent years, new theorems in the foundations of physics have reawakened interest in the idea of Wigner’s friend – an extrapolation of the Schrodinger’s cat thought experiment. In particular, two of us and co-workers showed that certain correlations predicted by quantum theory violate inequalities derived from a set of theory-independent assumptions which we called “Local Friendliness”. Our theorem is similar to the strongest versions of Bell’s theorem, but, crucially, it is an even stronger theorem, in that the inequalities are derived using a strictly smaller set of assumptions. However, unlike Bell’s theorem (but like all recent Wigner’s friend theorems), the Local Friendliness theorem has the technological assumption that it is possible to reverse an observation performed by a friend. This raises an obvious objection: this technological assumption is not plausible if the friend is a human being. Here we address that objection by proposing a (very challenging) experiment in which the technological assumption is plausible, for a being who could be broadly accepted as a friend. This being, QUALL-E by name, is a quantum computer running a human-level artificial intelligence algorithm. In addition to estimating just how challenging such an experiment would be, we formulate a new theorem, tailored for this experiment. We dub it a Thoughtful Local Friendliness theorem, as three of its assumptions are thought-related, including one that is explicitly called “Friendliness”. The intent of the new theorem is to give a clear goal for future experimentalists, and a clear motivation for trying to achieve that goal, by using assumptions that are widely held and not reliant on the universality of quantum mechanics. The popular stance that “quantum theory needs no interpretation” does not question any of our assumptions and so is ruled out by our theorem.

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[3] Adrian Kent, "The measurement postulates of quantum mechanics are not redundant", arXiv:2307.06191, (2023).

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[5] J. Allam and A. Matzkin, "From observer-dependent facts to frame-dependent measurement records in Wigner friend scenarios", arXiv:2304.09289, (2023).

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[7] Aníbal Utreras-Alarcón, Eric G. Cavalcanti, and Howard M. Wiseman, "Allowing Wigner's friend to sequentially measure incompatible observables", arXiv:2305.09102, (2023).

[8] Veronika Baumann and Caslav Brukner, "Observers in superposition and the no-signaling principle", arXiv:2305.15497, (2023).

[9] Veronika Baumann, "Classical information and collapse in Wigner's friend setups", arXiv:2308.08260, (2023).

[10] Davide Poderini, Giovanni Rodari, George Moreno, Emanuele Polino, Ranieri Nery, Alessia Suprano, Cristhiano Duarte, Fabio Sciarrino, and Rafael Chaves, "Device-independent witness for the nonobjectivity of quantum dynamics", Physical Review A 108 3, 032201 (2023).

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