Vladimirov, IgorPetersen, IanJames, MatthewLevine, W SStockbridge, R2024-01-18Jun 19-21978-1-61197-575-8http://hdl.handle.net/1885/311598This paper is concerned with the original risk-sensitive performance criterion for quantum stochastic systems and its recent quadraticexponential 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.This work is supported by the Air Force Office of Scientific Research (AFOSR) under agreement number FA2386-16-1-4065 and the Australian Research Council under grant DP180101805.application/pdfen-AU© 2019 by SIAM201910.1137/1.9781611975758.62022-10-02