FAU LMQ Research Spotlight: In quantum mechanics, there are two paths you must go by

In their recent work published in Quantum, our member Davide Lonigro and collaborators tackle a fundamental question about the nature of measurement in quantum mechanics: can we describe quantum measurements as the result of sampling a trajectory, as we do in classical physics?

Repeated measurements of a classical system produce multitime probability distributions that obey Kolmogorov consistency, ensuring that they arise from one underlying trajectory. In quantum mechanics, this consistency is typically violated: each measurement disturbs the system, breaking the link to a single objective path. But rather than abandoning the notion of trajectories, this paper proposes a surprising alternative: two trajectories suffice.

The authors prove a generalized version of the Kolmogorov extension theorem, adapted to the quantum setting using complex-valued bi-probability distributions—defined over pairs of trajectories. This work provides a new way to interpret quantum multitime statistics, offering a clearer theoretical foundation for understanding repeated measurements, a concept central to many quantum technologies.

For more information, see their publication in Quantum:

D. Lonigro, F. Sakuldee, Ł. Cywiński, D. Chruściński, and P. Szańkowski, “Double or nothing: a Kolmogorov extension theorem for (bi)probabilities in quantum mechanics”. Quantum 8 (2024), 1447.