On the separation principle of quantum control

Abstract

It is well known that quantum continuous observations and nonlinear filtering can be developed within the framework of the quantum stochastic calculus of Hudson-Parthasarathy. The addition of real-time feedback control has been discussed by many authors, but the foundations of the theory still appear to be relatively undeveloped. Here we introduce the notion of a controlled quantum flow, where feedback is taken into account by allowing the coefficients of the quantum stochastic differential equation to be adapted processes in the observation algebra. We then prove a separation theorem for quantum control: the admissible control that minimizes a given cost function is a memoryless function of the filter, provided that the associated Bellman equation has a sufficiently regular solution. Along the way we obtain results on existence and uniqueness of the solutions of controlled quantum filtering equations and on the innovations problem in the quantum setting.

24 pages; see also math-ph/0508006. An extended version of this paper is in preparation

References in corpus (5)

• Feedback control of quantum state reduction
• Adaptive homodyne measurement of optical phase
• Implementation of Grover's Quantum Search Algorithm in a Scalable System
• Bellman equations for optimal feedback control of qubit states
• Quantum filtering: a reference probability approach

Cited by in corpus (6)

• Construction of bilinear control Hamiltonians using the series product and quantum feedback
• Dynamic Quantum Games
• An Introduction to Quantum Filtering
• The law of large numbers for quantum stochastic filtering and control of many particle systems
• Quantum Filtering for Systems Driven by Fields in Single Photon States and Superposition of Coherent States using Non-Markovian Embeddings
• Control of Quantum Systems Despite Feedback Delay