2012/05/16 by Igor G. Vladimirov, Vladimirov, Igor G., Ian R. Petersen +1
Computer Science · Physics and Astronomy · #81Q15 #81Q93 #81S05 #81S22 #81S25 #93B28 #93C10 #93D09 #93E03 #93E15 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #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.1205.3566
openalex publication_date 2012/05/16 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
This paper is concerned with a stochastic dissipativity theory using\nquadratic-exponential storage functions for open quantum systems with\ncanonically commuting dynamic variables governed by quantum stochastic\ndifferential equations. The system is linearly coupled to external boson fields\nand has a quadratic Hamiltonian which is perturbed by nonquadratic functions of\nlinear combinations of system variables. Such perturbations are similar to\nthose in the classical Lur'e systems and make the quantum dynamics nonlinear.\nWe study their effect on the quantum expectation of the exponential of a\npositive definite quadratic form of the system variables. This allows\nconditions to be established for the risk-sensitive stochastic storage function\nof the quantum system to remain bounded, thus securing boundedness for the\nmoments of system variables of arbitrary order. These results employ a\nnoncommutative analogue of the Doleans-Dade exponential and a multivariate\npartial differential version of the Gronwall-Bellman lemma.\n