# AG Mathematische Physik, Davide Lonigro (FAU): Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics

**Davide Lonigro (FAU)**

**Double or nothing: a Kolmogorov extension theorem for multitime (bi)probabilities in quantum mechanics
**

Abstract:

The

multitime probability distributions obtained by repeatedly probing a

quantum system via the measurement of an observable generally violate

Kolmogorov’s consistency property. Therefore, one cannot interpret such

distributions as the result of the sampling of a single trajectory. 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.

Based on arXiv:2402.01218. Joint work with F. Sakuldee, Ł. Cywiński, D. Chruściński, and P. Szańkowski.

—