On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States

TL;DR

This paper advances the mathematical understanding of quantum stochastic filtering equations for mixed states, extending existing theories to include unbounded coupling operators in infinite-dimensional settings.

Contribution

It generalizes previous results by developing the theory for unbounded coupling operators, crucial for realistic quantum systems and infinite-dimensional models.

Findings

Extended the theory to unbounded coupling operators

Connected quantum filtering to mean field games

Provided rigorous mathematical foundations for complex quantum models

Abstract

Quantum filtering equations for mixed states were developed in 80th of the last century. Since then the problem of building a rigorous mathematical theory for these equations in the basic infinite-dimensional settings has been a challenging open mathematical problem. In a previous paper, the author developed the theory of these equations in the case of bounded coupling operators, including a new version that arises as the law of large numbers for interacting particles under continuous observation and thus leading to the theory of quantum mean field games. In this paper, the main body of these results is extended to the basic cases of unbounded coupling operators.