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Open access
Date
2019-01-31Type
- Conference Paper
ETH Bibliography
yes
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Abstract
We test the principles of classical modal logic in fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the Frauchiger-Renner theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show how most of the axioms of classical modal logic break down in quantum settings, and attempt to generalize them. Namely, we introduce constructions of trust and context, which highlight the importance of an exact structure of trust relations between agents. We propose a challenge to the community: to find conditions for the validity of trust relations, strong enough to exorcise the paradox and weak enough to still recover classical logic. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000341171Publication status
publishedExternal links
Book title
Proceedings of the 15th International Conference on Quantum Physics and LogicJournal / series
Electronic Proceedings in Theoretical Computer ScienceVolume
Pages / Article No.
Publisher
Open Publishing AssociationEvent
Organisational unit
03781 - Renner, Renato / Renner, Renato
Related publications and datasets
Is new version of: http://hdl.handle.net/20.500.11850/320520
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ETH Bibliography
yes
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