[PDF] Multi-point Gaussian States, Quadratic–Exponential Cost Functionals, and Large Deviations Estimates for Linear Quantum Stochastic Systems | Semantic Scholar (2024)

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A finite-horizon expansion is developed using the eigenbasis of their two-point commutator kernel with noncommuting position-momentum pairs as coefficients to obtain a Girsanov type representation for the quadratic-exponential functions of the system variables.

A randomised representation for the QEF is developed using a Karhunen–Loeve expansion of the quantum process on a bounded time interval over the eigenbasis of its two-point commutator kernel, with noncommuting position-momentum pairs as coefficients.

This paper is concerned with a class of open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices pertaining to finite-level systems, which results in a Hudson-Parthasarathy quantum stochastic differential equation (QSDE) whose drift and dispersion terms are affine and linear functions of the system variables.

An infinitesimal perturbation analysis of the quasi-characteristic function for the invariant quantum state of the nonlinear perturbed system is carried out and the resulting correction of the invariants states in the spatial frequency domain may find applications to their approximate computation, analysis of relaxation dynamics and non-Gaussian state generation in nonlinear quantum stochastic systems.

A Lie-algebraic correspondence between complex symplectic matrices and quadratic-exponential functions of system variables of a quantum harmonic oscillator is employed and is applicable to recursive computation of such moments.

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The gain matrices of the CQLQG optimal controller are shown to satisfy a quasi-separation property as a weaker quantum counterpart of the filtering/control decomposition of classical LQG controllers.

This paper discusses recent results concerning the synthesis of H-infinity optimal controllers for linear quantum systems in the coherent control case, and discusses the issue of physical realizability.

Links between the original risk-sensitive performance criterion for quantum control systems and its recent quadratic-exponential counterpart are considered and can be of use in providing a rational choice of the risk-sensitivity parameter in the context of robust quantum control with entropy theoretic quantification of statistical uncertainty in the system-field state.

Under suitable assumptions, the paper shows that the question of physical realizability is equivalent to a frequency domain (J,J) -unitary condition, which is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior.

A novel performance criterion is employed which seeks to minimize a combination of the average value and the variance of the output energy of the system per unit time.

The coherent quantum filtering (CQF) formulation is transformed into a constrained covariance control problem which is treated by using the Frechet differentiation of an appropriate Lagrange function with respect to the matrices of the filter.

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