Quantum complementarity and logical indeterminacy

Autor(en)

Caslav Brukner

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Journal

Natural Computing

Band

8

Seiten

449-453

Anzahl der Seiten

5

ISSN

1567-7818

DOI

https://doi.org/10.1007/s11047-009-9118-z

Publikationsdatum

2009

Peer-reviewed

Ja

ÖFOS 2012

1030 Physik, Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/207d4496-0e86-43ff-aaa9-0b759137c123