2013/08/28 by Hendra I. Nurdin, Nurdin, Hendra I. · 1 citation
Computer Science · Physics and Astronomy · #FOS: Electrical engineering #FOS: Mathematics #FOS: Physical sciences #Laser-Matter Interactions and Applications #Optimization and Control (math.OC) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1308.6062
openalex publication_date 2013/08/28 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
The purpose of this paper is to develop a model reduction theory for linear\nquantum stochastic systems that are commonly encountered in quantum optics and\nrelated fields, modeling devices such as optical cavities and optical\nparametric amplifiers, as well as quantum networks composed of such devices.\nResults are derived on subsystem truncation of such systems and it is shown\nthat this truncation preserves the physical realizability property of linear\nquantum stochastic systems. It is also shown that the property of complete\npassivity of linear quantum stochastic systems is preserved under subsystem\ntruncation. A necessary and sufficient condition for the existence of a\nbalanced realization of a linear quantum stochastic system under sympletic\ntransformations is derived. Such a condition turns out to be very restrictive\nand will not be satisfied by generic linear quantum stochastic systems, thus\nnecessary and sufficient conditions for relaxed notions of simultaneous\ndiagonalization of the controllability and observability Gramians of linear\nquantum stochastic systems under symplectic transformations are also obtained.\nThe notion of a quasi-balanced realization is introduced and it is shown that\nall asymptotically stable completely passive linear quantum stochastic systems\nhave a quasi-balanced realization. Moreover, an explicit bound for the\nsubsystem truncation error on a quasi-balanceable linear quantum stochastic\nsystem is provided. The results are applied in an example of model reduction in\nthe context of low-pass optical filtering of coherent light using a network of\noptical cavities.\n