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Quantum paradoxes show that quantum statistics can exceed the limits ofpositive joint probabilities for physical properties that cannot be measuredjointly. It is therefore impossible to describe the relations between thedifferent physical properties of a quantum system by assigning joint realitiesto their observable values. Instead, recent experimental results obtained byweak measurements suggest that non-classical correlations could be expressed bycomplex valued quasi-probabilities, where the phases of the complexprobabilities express the action of transformations between the non-commutingproperties (H. F. Hofmann, New J. Phys. 13, 103009 (2011)). In these relations,negative probabilities necessarily emerge whenever the physical propertiesinvolved are related to each other by half-periodic transformations, since suchtransformations are characterized by action phases of Pi in their complexprobabilities. It is therefore possible to trace the failure of realistassumptions back to a fundamental and universally valid relation betweenstatistics and dynamics that associates half-periodic transformations withnegative probabilities.

How quantum paradoxes originate from the non-classical statistics of physical properties related to each other by half-periodic transformations