Vladimirov, I.G. A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems. Entropy2023, 25, 1179.
Vladimirov, I.G. A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems. Entropy 2023, 25, 1179.
Vladimirov, I.G. A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems. Entropy2023, 25, 1179.
Vladimirov, I.G. A Transverse Hamiltonian Approach to Infinitesimal Perturbation Analysis of Quantum Stochastic Systems. Entropy 2023, 25, 1179.
Abstract
This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.
Copyright:
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