  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.
