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arXiv:1904.06247 · New Journal of Physics

Multi-agent paradoxes beyond quantum theory

V. Vilasini, Nuriya Nurgalieva, Lídia del Rio

Published Oct 21, 2019• 17 citations
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Abstract

Which theories lead to a contradiction between simple reasoning principles and modelling observers’ memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory (Frauchiger and Renner 2018 Nat. Commun. 9 3711). Here we generalize the conditions of the Frauchiger–Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs) (Hardy 2001 arXiv: quant-ph/0101012 ; Barrett 2007 Phys. Rev. A 75 032304). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box (Popescu and Rohrlich 1994 Found. Phys. 24 379–85), which is stronger than the quantum paradox, in that it does not rely on post-selection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers’ memories may evolve in box world, in a way consistent with Barrett’s criteria for allowed operations (Barrett 2007 Phys. Rev. A 75 032304; Gross et al 2010 Phys. Rev. Lett. 104 080402). Ordinary readers, forgive my paradoxes: one must make them when one reflects; and whatever you may say, I prefer being a man with paradoxes than a man with prejudices. Jean-Jacques Rousseau, Emile or On Education

DOI
10.1088/1367-2630/ab4fc4

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Which theories lead to a contradiction between simple reasoning principles and modelling observers’ memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory (Frauchiger and Renner 2018 Nat. Commun. 9 3711). Here we generalize the conditions of the Frauchiger–Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs) (Hardy 2001 arXiv: quant-ph/0101012 ; Barrett 2007 Phys. Rev. A 75 032304). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box (Popescu and Rohrlich 1994 Found. Phys. 24 379–85), which is stronger than the quantum paradox, in that it does not rely on post-selection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers’ memories may evolve in box world, in a way consistent with Barrett’s criteria for allowed operations (Barrett 2007 Phys. Rev. A 75 032304; Gross et al 2010 Phys. Rev. Lett. 104 080402). Ordinary readers, forgive my paradoxes: one must make them when one reflects; and whatever you may say, I prefer being a man with paradoxes than a man with prejudices. Jean-Jacques Rousseau, Emile or On Education
Which theories lead to a contradiction between simple reasoning principles and modelling observers' memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory (Frauchiger and Renner 2018 Nat. Commun. 9 3711). Here we generalize the conditions of the Frauchiger–Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs) (Hardy 2001 arXiv:quant-ph/0101012; Barrett 2007 Phys. Rev. A 75 032304). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box (Popescu and Rohrlich 1994 Found. Phys. 24 379–85), which is stronger than the quantum paradox, in that it does not rely on post-selection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers' memories may evolve in box world, in a way consistent with Barrett's criteria for allowed operations (Barrett 2007 Phys. Rev. A 75 032304; Gross et al 2010 Phys. Rev. Lett. 104 080402).
This paper provides a comprehensive analysis of the Frauchiger–Renner paradox (2018), a significant thought experiment that demonstrates a logical contradiction arising when standard quantum mechanics is applied to nested observers. Building on Wigner’s friend scenario, it examines the formal setup, derives the contradiction from assumptions of universality, the Born rule, and self-consistency in multi-agent reasoning, and evaluates proposed resolutions across major interpretations of quantum mechanics (Copenhagen, Everettian/many-worlds, relational, QBism, decoherent histories, and objective collapse theories). The work explores historical context, epistemological implications for observation, objectivity, and intersubjectivity, as well as recent experimental probes and theoretical refinements. It argues that the paradox reveals deep tensions in applying quantum theory to complex, self-referential scenarios involving observers (2026).
This thesis reports progress in the analysis of causality and multi-agent logical paradoxes in quantum and post-quantum theories. These research areas are highly relevant for the foundations of physics as well as the development of quantum technologies. In the first part, focussing on causality, we develop techniques for using generalised entropies to analyse distinctions between classical and non-classical causal structures. We derive new properties of Tsallis entropies of systems that follow from the relevant causal structure, and apply these to obtain new necessary constraints for classicality in the Triangle causal structure. Supplementing the method with the post-selection technique, we provide evidence that Shannon and Tsallis entropic constraints are insufficient for detecting non-classicality in Bell scenarios with non-binary outcomes. This points to the need for better methods of characterising correlations in non-classical causal structures. Further, we investigate the relationships between causality and space-time by developing a framework for modelling cyclic and fine-tuned influences in non-classical theories. We derive necessary and sufficient conditions for such causal models to be compatible with a space-time structure and for ruling out operationally detectable causal loops. In particular, this provides an operational framework for analysing post-quantum theories admitting jamming non-local correlations. In the second part, we investigate multi-agent logical paradoxes such as the Frauchiger-Renner paradox and develop a framework for analysing such paradoxes in arbitrary physical theories. Applying this to box world, a post-quantum theory, we derive a stronger paradox that does not rely on post-selection. Our results reveal that reversible evolution of agents' memories is not necessary for deriving multi-agent paradoxes, and that certain forms of contextuality might be.
How can we consistently model the knowledge of the natural world provided by physical theories? Philosophers frequently use epistemic logic to model reasoning and knowledge abstractly, and to formally study the ramifications of epistemic assumptions. One famous example is Fitch's paradox, which begins with minimal knowledge axioms and derives the counter-intuitive result that agent knows every true statement. Accounting for knowledge that arises from physical theories complicates matters further. For example, quantum mechanics allows observers to model other agents as quantum systems themselves, and to make predictions about measurements performed on each others' memories. Moreover, complex thought experiments in which agents' memories are modelled as quantum systems show that multi-agent reasoning chains can yield paradoxical results. Here, we bridge the gap between quantum paradoxes and foundational problems in epistemic logic, by relating the assumptions behind the recent Frauchiger-Renner quantum thought experiment and the axioms for knowledge used in Fitch's knowability paradox. Our results indicate that agents' knowledge of quantum systems must violate at least one of the following assumptions: it cannot be distributive over conjunction, have a kind of internal continuity, and yield a constructive interpretation all at once. Indeed, knowledge provided by quantum mechanics apparently contradicts traditional notions of how knowledge behaves; for instance, it may not be possible to universally assign objective truth values to claims about agent knowledge. We discuss the relations of this work to results in quantum contextuality and explore possible modifications to standard epistemic logic that could make it consistent with quantum theory.
Abstract We take a fresh look at Wigner’s Friend thought-experiment and some of its more recent variants and extensions, such as the Frauchiger-Renner (FR) Paradox. We discuss various solutions proposed in the literature, focusing on a few questions: What is the correct epistemic interpretation of the multiplicity of state assignments in these scenarios? Under which conditions can one include classical observers into the quantum state descriptions, in a way that is still compatible with traditional Quantum Mechanics? Under which conditions can one system be admitted as an additional ‘observer’ from the perspective of another background observer? When can the standard axioms of multi-agent Epistemic Logic (that allow “knowledge transfer” between agents) be applied to quantum-physical observers? In the last part of the paper, we propose a new answer to these questions, sketch a particular formal implementation of this answer, and apply it to obtain a principled solution to Wigner Friend-type paradoxes.