Quantum Pontryagin Principle under Continuous Measurements and Feedback

TL;DR

This paper develops a quantum Pontryagin maximum principle for systems under continuous measurement and feedback, providing a framework for quantum control that includes a new LQG scheme suitable for practical applications.

Contribution

It introduces a quantum Pontryagin principle for continuous measurements and feedback, including derivations in multiple pictures and a new LQG scheme for control.

Findings

Derived the quantum Pontryagin maximum principle in Schrödinger and Heisenberg pictures.

Established a LQG scheme for quantum control under continuous measurements.

Applicable to quantum systems in mixed states with compatible output events.

Abstract

In this note 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 Schr\"{o}dinger picture and Heisenberg picture, in particular in statistical moment coordinates. To avoid solving stochastic equations we derive a LQG scheme which is more suitable for control purposes.