What the complex joint probabilities observed in weak measurements can tell us about quantum physics
arXiv:1303.0078 · doi:10.1063/1.4903083
Abstract
Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be interpreted as complex joint probabilities of the two non-commuting measurement outcomes. Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex conditional probabilities relating the new measurement to the possible combinations of measurement outcomes used in the characterization of the quantum state. We can therefore conclude that the complex conditional probabilities observed in weak measurements describe fundamental state-independent relations between non-commuting properties that represent the most fundamental form of universal laws in quantum physics.
This short note (2 pages) is a contribution to the proceedings of QCMC 2012 held in Vienna, Austria, July 30th to August 3rd 2012. It is intended as a short motivational discussion of the significance that recent results on complex probabilities might have for our general understanding of the laws of physics