Linear quantum feedback networks with squeezing components

The aim of this paper is to extend linear quantum dynamical network theory to include static Bogoliubov components (such as squeezers). Within this integrated quantum network theory we provide general methods for cascade or series connections, as well as feedback interconnections using linear fractional transformations. In addition, we define input-output maps and transfer functions in this quantum context, show how they can be useful. We also discuss the underlying group structure in this theory arising from series interconnection.

[1]  M. R. James,et al.  Quantum Feedback Networks: Hamiltonian Formulation , 2008, 0804.3442.

[2]  David Shale,et al.  LINEAR SYMMETRIES OF FREE BOSON FIELDS( , 1962 .

[3]  Applications of canonical transformations , 2004, quant-ph/0410209.

[4]  Matthew R. James,et al.  The Series Product and Its Application to Quantum Feedforward and Feedback Networks , 2007, IEEE Transactions on Automatic Control.

[5]  Hendra Ishwara Nurdin,et al.  Network Synthesis of Linear Dynamical Quantum Stochastic Systems , 2008, SIAM J. Control. Optim..

[6]  Timothy C. Ralph,et al.  A Guide to Experiments in Quantum Optics , 1998 .

[7]  A. Neumaier,et al.  LETTER TO THE EDITOR: Explicit effective Hamiltonians for general linear quantum-optical networks , 2003 .

[8]  M. Zwaan An introduction to hilbert space , 1990 .

[9]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .

[10]  M.R. James,et al.  $H^{\infty}$ Control of Linear Quantum Stochastic Systems , 2008, IEEE Transactions on Automatic Control.

[11]  M. R. James,et al.  Squeezing Components in Linear Quantum Feedback Networks , 2009, 0906.4860.

[12]  Hidenori Kimura,et al.  Transfer function approach to quantum control-part I: Dynamics of quantum feedback systems , 2003, IEEE Trans. Autom. Control..

[13]  Ian R. Petersen,et al.  Coherent H∞ control for a class of linear complex quantum systems , 2009, 2009 American Control Conference.

[14]  Robin L. Hudson,et al.  Quantum Ito's formula and stochastic evolutions , 1984 .

[15]  M.R. James,et al.  H∞ Control of Linear Quantum Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[16]  M. Yanagisawa,et al.  Linear quantum feedback networks , 2008 .

[17]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[18]  Collett,et al.  Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation. , 1985, Physical review. A, General physics.