Quantum Pontryagin principle under continuous measurements

In this paper, we develop the theory of the quantum Pontryagin principle for continuous measurements and feedback. The analysis is carried out under the assumption of compatible events in the output channel. The plant is a quantum system, which generally is in a mixed state, coupled to a continuous...

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Bibliographic Details
Published in:Journal of mathematical physics 2020-10, Vol.61 (10)
Main Authors: Mulero-Martínez, J. I., Molina-Vilaplana, J.
Format: Article
Language:English
Subjects:
Harmonic oscillators
Linear quadratic Gaussian control
Maximum principle
Physics
Pontryagin principle
Quantum theory
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Summary:In this paper, we develop the theory of the quantum Pontryagin principle for continuous measurements and feedback. The analysis is carried out under the assumption of compatible events in the output channel. The plant is a quantum system, which generally is in a mixed state, coupled to a continuous measurement channel. The Pontryagin maximum principle is derived in both the Schrödinger picture and Heisenberg picture, in particular, in statistical moment coordinates. To avoid solving stochastic equations, we derive a linear-quadratic-Gaussian scheme, which is more suitable for control purposes. Finally, we use the quantum harmonic oscillator as a concrete example to illustrate the performance of the controller.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0011343