Best of NJP 2010: "Logical independence and quantum randomness"
04. Apr 2011 — The article 'Logical independence and quantum randomness' has been selected to appear in the New Journal of Physics (NJP) ‘Best of 2010’ collection. This collection is a special showcase of papers that have been selected to represent the breadth and excellence of the work published in the journal last year.
"Logical independence and quantum randomness" by T. Paterek, J. Kofler, R. Prevedel, P. Klimek, M. Aspelmeyer, A. Zeilinger and C. Brukner
New J. Phys. 12, 013019, doi: 10.1088/1367-2630/12/1/013019
Abstract: 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.
NJP Best of 2010