On quantum stochastic master equations
Year: 2025
Type: article
Abstract: Stochastic Master equations or quantum filtering equations for mixed states are well known objects in quantum physics. Building a mathematically rigorous theory of these equations in infinite-dimensional spaces has been a long standing open problem. The first objective of this paper is to give a solution to this problem under the assumption of bounded operators providing coupling with environment (or a measurement device). Furthermore, recently the author built the theory of the law of large number limit for continuously observed interacting quantum particle systems leading to quantum mean-field games. These limits are described by certain nontrivial extensions of quantum stochastic master equations that can be looked at as infinite-dimensional operator-valued McKean-Vlasov diffusions. The second objective of this paper is to provide a well-posedness result for these new class of McKean-Vlasov diffusions.
DOI: 10.1214/25-ejp1322
Author: Vassili N. Kolokoltsov
Institution: Lomonosov Moscow State University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $675
OpenAlex ID: W4409064832