Quantum paradoxes show that quantum statistics can exceed the limits of positive joint probabilities for physical properties that cannot be measured jointly. It is therefore impossible to describe the relations between the different physical properties of a quantum system by assigning joint realities to their observable values. Instead, recent experimental results obtained by weak measurements suggest that nonclassical correlations could be expressed by complex valued quasiprobabilities, where the phases of the complex probabilities express the action of transformations between the noncommuting properties [H. F. Hofmann, New J. Phys. 13, 103009 (2011)]. In these relations, negative probabilities necessarily emerge whenever the physical properties involved are related to each other by half-periodic transformations, since such transformations are characterized by action phases of $\pi$ in their complex probabilities. It is therefore possible to trace the failure of realist assumptions back to a fundamental and universally valid relation between statistics and dynamics that associates half-periodic transformations with negative probabilities.

• Received 12 November 2014
• Revised 25 March 2015

DOI:https://doi.org/10.1103/PhysRevA.91.062123