Seminarium KMMF "Teoria Dwoistości"

The multitime probability distributions that describe the sequential measurements of a quantum observable generally violate Kolmogorov's consistency property. Therefore, one cannot interpret such distributions as the result of the sampling of a single trajectory representing the observable. We show that, nonetheless, they do result from the sampling of one pair of trajectories. In this sense, rather than give up on trajectories, quantum mechanics requires to double down on them. To this purpose, we prove a generalization of the Kolmogorov extension theorem that applies to families of complex-valued bi-probability distributions (that is, defined on pairs of elements of the original sample spaces), and we employ this result in the quantum mechanical scenario.[1] D. Lonigro, F. Sakuldee, Ł. Cywiński, D. Chruściński, and P. Szańkowski, Quantum 8, 1447 (2024)