Lie-algebraic connections between two classes of risk-sensitive performance criteria for linear quantum stochastic systems
For researchers in quantum robust control and filtering, this work provides a theoretical bridge between two cost functionals, potentially enabling better optimization and robustness analysis.
This paper establishes a Lie-algebraic connection between two risk-sensitive performance criteria for linear quantum stochastic systems, enabling the transfer of useful properties between them and facilitating state-space equations for computation and optimization.
This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadratic-exponential counterpart. These functionals are of different structure because of the noncommutativity of quantum variables and have their own useful features such as tractability of evolution equations and robustness properties. We discuss a Lie algebraic connection between these two classes of cost functionals for open quantum harmonic oscillators using an apparatus of complex Hamiltonian kernels and symplectic factorizations. These results are aimed to extend useful properties from one of the classes of risk-sensitive costs to the other and develop state-space equations for computation and optimization of these criteria in quantum robust control and filtering problems.