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

Fuente: arXiv
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Main Author: Kolokoltsov, Vassili N
Format: Preprint
Published: 2025
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author Kolokoltsov, Vassili N
author_facet Kolokoltsov, Vassili N
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2505_14605
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States
Kolokoltsov, Vassili N
Mathematical Physics
60H15, 60K35, 81P15, 81Q93, 93E11
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.
title On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States
topic Mathematical Physics
60H15, 60K35, 81P15, 81Q93, 93E11
url https://arxiv.org/abs/2505.14605