TY - JOUR
AB - We propose a link between logical independence and quantum\r\nphysics. We demonstrate that quantum systems in the eigenstates of Pauli\r\ngroup operators are capable of encoding mathematical axioms and show that\r\nPauli group quantum measurements are capable of revealing whether or not a\r\ngiven proposition is logically dependent on the axiomatic system. Whenever\r\na mathematical proposition is logically independent of the axioms encoded\r\nin the measured state, the measurement associated with the proposition gives\r\nrandom outcomes. This allows for an experimental test of logical independence.\r\nConversely, it also allows for an explanation of the probabilities of random\r\noutcomes observed in Pauli group measurements from logical independence\r\nwithout invoking quantum theory. The axiomatic systems we study can be\r\ncompleted and are therefore not subject to Gödel’s incompleteness theorem.
AU - Paterek, T.
AU - Kofler, J.
AU - Prevedel, R.
AU - Klimek, P.
AU - Aspelmeyer, M.
AU - Zeilinger, A.
AU - Brukner, Č.
DA - 2010/01/20/
JF - New Journal of Physics
PY - 2010
SE - 2010/01/20/
TI - Logical independence and quantum randomness
UR - http://iopscience.iop.org/1367-2630/12/1/013019
ER -