The Library
Dynamic quantum games
Tools
Kolokoltsov, Vassili N. (2022) Dynamic quantum games. Dynamic Games and Applications, 12 . pp. 552-573. doi:10.1007/s13235-021-00389-w ISSN 2153-0785.
|
PDF
WRAP-dynamic-quantum-games-Kolokoltsov-2021.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (536Kb) | Preview |
Official URL: http://dx.doi.org/10.1007/s13235-021-00389-w
Abstract
Quantum games represent the really twenty-first century branch of game theory, tightly linked to the modern development of quantum computing and quantum technologies. The main accent in these developments so far was made on stationary or repeated games. In this paper, we aim at initiating the truly dynamic theory with strategies chosen by players in real time. Since direct continuous observations are known to destroy quantum evolutions (so-called quantum Zeno paradox), the necessary new ingredient for quantum dynamic games must be the theory of non-direct observations and the corresponding quantum filtering. Apart from the technical problems in organizing feedback quantum control in real time, the difficulty in applying this theory for obtaining mathematically amenable control systems is due partially to the fact that it leads usually to rather non-trivial jump-type Markov processes and/or degenerate diffusions on manifolds, for which the corresponding control is very difficult to handle. The starting point for the present research is the remarkable discovery (quite unexpected, at least to the author) that there exists a very natural class of homodyne detections such that the diffusion processes on projective spaces resulting by filtering under such arrangements coincide exactly with the standard Brownian motions (BM) on these spaces. In some cases, one can even reduce the process to the plain BM on Euclidean spaces or tori. The theory of such motions is well studied making it possible to develop a tractable theory of related control and games, which can be at the same time practically implemented on quantum optical devices.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Library of Congress Subject Headings (LCSH): | Quantum theory, Game theory , Stochastic differential equations, Brownian motion processes , Riemannian manifolds | ||||||||
Journal or Publication Title: | Dynamic Games and Applications | ||||||||
Publisher: | Birkhaeuser Science | ||||||||
ISSN: | 2153-0785 | ||||||||
Official Date: | June 2022 | ||||||||
Dates: |
|
||||||||
Volume: | 12 | ||||||||
Page Range: | pp. 552-573 | ||||||||
DOI: | 10.1007/s13235-021-00389-w | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||||
Date of first compliant deposit: | 27 July 2021 | ||||||||
Date of first compliant Open Access: | 28 July 2021 | ||||||||
RIOXX Funder/Project Grant: |
|
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year