dorsal/arxiv
View SchemaMeasurement, Filtering and Control in Quantum Open Dynamical Systems
| Authors | V. P. Belavkin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0208108 |
| URL | https://arxiv.org/abs/quant-ph/0208108 |
| Journal | Now published in: Rep. on Math. Phys. 45 No3 (1999) 353--420 |
Abstract
A Markovian model for a quantum automata, i.e. an open quantum dynamical discrete-time system with input and output channels and a feedback, is described. A dynamical theory of quantum discrete-time adaptive measurements and multi-stage quantum statistical decisions is developed and applied to the optimal feedback control problem for the quantum dynamical objects. Quantum analogies of Stratonovich non-stationary filtering, and Bellman quantum dynamical programming in the discrete time are derived. A Gaussian Langevin model of the quantum one-dimensional linear Markovian dynamical system matched with a quantum linear transmission line as an input-output quantum noisy channel is studied. The optimal quantum multi-stage decision rule consisting of a classical linear optimal control strategy and the quantum optimal filtering of the noise is found. The latter contains the optimal quantum coherent measurement on the output of the line and the recursive processing by the Kalman filter. A time-continuous limit of the above model is considered, and the quantum nondemolition measurement, time-continuous filtering and the optimal dynamical programming are found in this limit. All the results are illustrated by an example of the optimal control problem for a quantum open oscillator matched to a quantum transmission line.
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"abstract": "A Markovian model for a quantum automata, i.e. an open quantum dynamical\ndiscrete-time system with input and output channels and a feedback, is\ndescribed. A dynamical theory of quantum discrete-time adaptive measurements\nand multi-stage quantum statistical decisions is developed and applied to the\noptimal feedback control problem for the quantum dynamical objects. Quantum\nanalogies of Stratonovich non-stationary filtering, and Bellman quantum\ndynamical programming in the discrete time are derived.\n A Gaussian Langevin model of the quantum one-dimensional linear Markovian\ndynamical system matched with a quantum linear transmission line as an\ninput-output quantum noisy channel is studied. The optimal quantum multi-stage\ndecision rule consisting of a classical linear optimal control strategy and the\nquantum optimal filtering of the noise is found. The latter contains the\noptimal quantum coherent measurement on the output of the line and the\nrecursive processing by the Kalman filter.\n A time-continuous limit of the above model is considered, and the quantum\nnondemolition measurement, time-continuous filtering and the optimal dynamical\nprogramming are found in this limit. All the results are illustrated by an\nexample of the optimal control problem for a quantum open oscillator matched to\na quantum transmission line.",
"arxiv_id": "quant-ph/0208108",
"authors": [
"V. P. Belavkin"
],
"categories": [
"quant-ph"
],
"journal_ref": "Now published in: Rep. on Math. Phys. 45 No3 (1999) 353--420",
"title": "Measurement, Filtering and Control in Quantum Open Dynamical Systems",
"url": "https://arxiv.org/abs/quant-ph/0208108"
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