Quantum complementarity and logical indeterminacy

Details Quantum complementarity and logical indeterminacy Quantum complementarity and logical indeterminacy

2009-01-21

arxiv.org/abs/0901.3327v2

Nat. Comp. 8, 1567 (2009).

Physics

Quantum Physics

4 pages, 1 figure, printed version

Scientific paper

10.1007/s11047-009-9118-z

Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system. I will show that certain mathematical propositions on a d-valent function of a binary argument can be encoded in d-dimensional quantum states of mutually unbiased basis (MUB) sets, and truth values of the propositions can be tested in MUB measurements. I will then show that a proposition is undecidable within the system of axioms encoded in the state, if and only if the measurement associated with the proposition gives completely random outcomes.

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