Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control

Details Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control

2005-02-24

arxiv.org/abs/quant-ph/0502155v2

J. Opt. B: Quantum Semiclass. Opt. 7 S237-S244 (2005)

Physics

Quantum Physics

14 pages, no figures (modified notation)

Scientific paper

10.1088/1464-4266/7/10/006

We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.

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