In:
Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 4 ( 2020-04-20), p. 255-
Abstract:
In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More generally, it does not hold in any theory of stochastic processes -- classical, quantum or beyond -- that does not just describe passive observations, but allows for active interventions. Such processes form the basis of the study of causal modelling across the sciences, including in the quantum domain. To date, these frameworks have lacked a conceptual underpinning similar to that provided by Kolmogorov’s theorem for classical stochastic processes. We prove a generalized extension theorem that applies to a l l theories of stochastic processes, putting them on equally firm mathematical ground as their classical counterpart. Additionally, we show that quantum causal modelling and quantum stochastic processes are equivalent. This provides the correct framework for the description of experiments involving continuous control, which play a crucial role in the development of quantum technologies. Furthermore, we show that the original extension theorem follows from the generalized one in the correct limit, and elucidate how a comprehensive understanding of general stochastic processes allows one to unambiguously define the distinction between those that are classical and those that are quantum.
Type of Medium:
Online Resource
ISSN:
2521-327X
DOI:
10.22331/q-2020-04-20-255
Language:
English
Publisher:
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Publication Date:
2020
detail.hit.zdb_id:
2931392-2
