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Open Quantum Systems Decoherence

Quantum complementarity and logical indeterminacy

arXiv

Authors: Caslav Brukner

Year

2009

Paper ID

9195

Status

Preprint

Abstract Read

~2 min

Abstract Words

109

Citations

N/A

Abstract

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.

Why This Paper Matters

This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
It adds a 2009 reference point for readers tracking recent quantum research.
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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0901.3327 [2] arXiv https://arxiv.org/abs/0901.3327 [3] Publisher https://arxiv.org/abs/0901.3327

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