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Abstract: Whenever a mathematical proposition to be proved requires more informationthan it is contained in an axiomatic system, it can neither be proved nordisproved, i.e. it is undecidable, or logically undetermined, within thisaxiomatic system. I will show that certain mathematical propositions on ad-valent function of a binary argument can be encoded in d-dimensional quantumstates of mutually unbiased basis MUB sets, and truth values of thepropositions can be tested in MUB measurements. I will then show that aproposition is undecidable within the system of axioms encoded in the state, ifand only if the measurement associated with the proposition gives completelyrandom outcomes.

Author: Caslav Brukner

Source: https://arxiv.org/

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