Logical independence and quantum randomness

Autor(en)

Tomasz Paterek, Johannes Kofler, Robert Prevedel, Peter Klimek, Markus Aspelmeyer, Anton Zeilinger, Caslav Brukner

Abstrakt

We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Gödel's incompleteness theorem.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Österreichische Akademie der Wissenschaften (ÖAW), University of Waterloo (UW), Medizinische Universität Wien

Journal

New Journal of Physics

Band

12

Anzahl der Seiten

10

ISSN

1367-2630

DOI

https://doi.org/10.1088/1367-2630/12/1/013019

Publikationsdatum

2010

Peer-reviewed

Ja

ÖFOS 2012

103025 Quantenmechanik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/6b05430c-3139-4b45-8c9e-0827e950c7d3