Linear Quantum Feedback Networks

Abstract

The mathematical theory of quantum feedback networks has recently been developed for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical systems Markovian systems with instantaneous feedback connections, that the transfer functions can be deduced and agree with the algebraic rules obtained in the nonlinear case. Using these rules, we derive the the transfer functions for linear quantum systems in series, in cascade, and in feedback arrangements mediated by beam splitter devices.

19 pages, Latex figures in text

References in corpus (7)

• Coherent quantum LQG control
• Coherent-feedback quantum control with a dynamic compensator
• Polarization squeezing by optical Faraday rotation
• Suppression of Classical and Quantum Radiation Pressure Noise via Electro-Optic Feedback
• Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem
• A quantum stochastic calculus approach to modeling double-pass atom-field coupling
• Incoherent Quantum Control

Cited by in corpus (46)

• Quantum feedback: theory, experiments, and applications
• Modeling and Control of Quantum Systems: An Introduction
• Squeezing Components in Linear Quantum Feedback Networks
• N-Photon wave packets interacting with an arbitrary quantum system
• The SLH framework for modeling quantum input-output networks
• Time-delayed quantum feedback control
• Enhancement of Field Squeezing Using Coherent Feedback
• Robust Stability of Uncertain Quantum Systems
• System identification for passive linear quantum systems
• Zero-dynamics principle for perfect quantum memory in linear networks
• Synthesis of linear quantum stochastic systems via quantum feedback networks
• Feedback control in quantum optics: an overview of experimental breakthroughs and areas of application
• Pure Gaussian state generation via dissipation: A quantum stochastic differential equation approach
• Decoherence-free linear quantum subsystems
• Comparison between continuous- and discrete-mode coherent feedback for the Jaynes-Cummings model
• Coherent feedback control in quantum transport
• Noise suppression of on-chip mechanical resonators by chaotic coherent feedback
• Interferometric modulation of quantum cascade interactions
• Trapped Modes in Linear Quantum Stochastic Networks with Delays
• Feedback Network Models for Quantum Transport
• Singular Perturbation Approximations for General Linear Quantum Systems
• A Popov Stability Condition for Uncertain Linear Quantum Systems
• Optimal control for perfect state transfer in linear quantum memory
• Quantum Robust Stability of a Small Josephson Junction in a Resonant Cavity
• The Series Product and Its Application to Quantum Feedforward and Feedback Networks
• Coherent-Classical Estimation for Linear Quantum Systems
• Coherent-Classical Estimation versus Purely-Classical Estimation for Linear Quantum Systems
• Robust Stability of Quantum Systems with Nonlinear Dynamic Uncertainties
• Non-Markovian Quantum Feedback Networks I: Quantum Transmission Lines, Lossless Bounded Real Property and Limit Markovian Channels
• The Global versus Local Hamiltonian Description of Quantum Input-Output Theory
• Robust $H_{\infty }$ Estimation of Uncertain Linear Quantum Systems
• Non-Markovian Quantum Feedback Networks II: Controlled Flows
• A Realization Method for Transfer Functions of Linear Quantum Stochastic Systems Using Static Networks for Input/Output Processing and Feedback
• Causality Violation and Nonlinear Quantum Mechanics
• A Survey of Riccati Equation Results in Negative Imaginary Systems Theory and Quantum Control Theory
• Characteristic Operator Functions for Quantum Input-Plant-Output Models & Coherent Control
• Coherent control in quantum transport: amplification, filtering and switching at finite bias
• Quantum state transfer for multi-input linear quantum systems
• Quantum coherent feedback control of an N-level atom with multiple excitations
• Tangential Interpolatory Projection for Model Reduction of Linear Quantum Stochastic Systems
• Implementation of Bilinear Hamiltonian Interactions between Linear Quantum Stochastic Systems via Feedback
• Formulae for entanglement in a linear coherent feedback network of multiple nondegenerate optical parametric amplifiers: the infinite bandwidth case
• Signal Flows in Non-Markovian Linear Quantum Feedback Networks
• Robust Stability Analysis of an Optical Parametric Amplifier Quantum System
• A Systems Theory Approach to the Synthesis of Minimum Noise Phase-Insensitive Quantum Amplifiers
• Low Frequency Approximation for a class of Linear Quantum Systems using Cascade Cavity Realization