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Weak measurements performed between quantum state preparation andpost-selection result in complex values for self-adjoint operators,corresponding to complex conditional probabilities for the projections onspecific eigenstates. In this paper, it is shown that the complex phases ofthese weak conditional probabilities describe the dynamic response of thesystem to unitary transformations. Quantum mechanics thus unifies thestatistical overlap of different states with the dynamical structure oftransformations between these states. Specifically, it is possible to identifythe phase of weak conditional probabilities directly with the action of aunitary transform that maximizes the overlap of initial and final states. Thisaction provides a quantitative measure of how much quantum correlations candiverge from the deterministic relations between physical properties expectedfrom classical physics or hidden variable theories. In terms of quantuminformation, the phases of weak conditional probabilities thus represent thelogical tension between sets of three quantum states that is at the heart ofquantum paradoxes.

On the role of complex phases in the quantum statistics of weak measurements