2019/11/04 by Igor G. Vladimirov, Vladimirov, Igor G., Ian R. Petersen +3
Computer Science · Physics and Astronomy · #34L10 #45P05 #60G15 #81P16 #81Q10 #81Q93 #81S05 #81S22 #81S25 #Advanced Thermodynamics and Statistical Mechanics #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC) #Probability (math.PR) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1911.01539
openalex publication_date 2019/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with multimode open quantum harmonic oscillators and\nquadratic-exponential functionals (QEFs) as quantum risk-sensitive performance\ncriteria. Such systems are described by linear quantum stochastic differential\nequations driven by multichannel bosonic fields. We develop a finite-horizon\nexpansion for the system variables using the eigenbasis of their two-point\ncommutator kernel with noncommuting position-momentum pairs as coefficients.\nThis quantum Karhunen-Loeve expansion is used in order to obtain a Girsanov\ntype representation for the quadratic-exponential functions of the system\nvariables. This representation is valid regardless of a particular system-field\nstate and employs the averaging over an auxiliary classical Gaussian random\nprocess whose covariance operator is defined in terms of the quantum commutator\nkernel. We use this representation in order to relate the QEF to the\nmoment-generating functional of the system variables. This result is also\nspecified for the invariant multipoint Gaussian quantum state when the\noscillator is driven by vacuum fields.\n