The series product and its application to quantum feedforward and feedback networks

IEEE Transactions on Automatic Control

Volumn 54, Issue 11, 2009, Pages 2530-2544

  Gough, John ^a   James, Matthew R ^b  

^a ABERYSTWYTH UNIVERSITY   (United Kingdom)

^b AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

Cascade; Feedback; Feedforward; Quantum control; Quantum networks; Quantum noise; Series

Indexed keywords

CASCADE; FEED-FORWARD; QUANTUM CONTROL; QUANTUM NETWORKS; SERIES;

CASCADE CONNECTIONS; CONTROL THEORY; QUANTUM NOISE; QUANTUM THEORY; TELECOMMUNICATION NETWORKS;

ALGEBRA;

EID: 76249086972     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2031205     Document Type: Article

References (27)

1. V. P. Belavkin, "Quantum stochastic calculus and quantum nonlinear filtering", J. Multivariate Anal., vol. 42, pp. 171-201, 1992.
2. L. Bouten, R. Van Handel, and M. R. James, "An introduction to quantum filtering", SIAM J. Control Optim., vol. 46, no. 6, pp. 2199-2241, 2007.
3. H. J. Carmichael, "Quantum trajectory theory for cascaded open systems", Phys. Rev. Lett, vol. 70, no. 15, pp. 2273-2276, 1993.
4. C. D'Helon and M. R. James, "Stability, gain, and robustness in quantum feedback networks", Phys. Rev. A, vol. 73, p. 053803, 2006.
5. R. J. Elliott, Stochastic Calculus and Applications. New York: Springer Verlag, 1982.
6. C. W. Gardiner, "Driving a quantum system with the output field from another driven quantum system", Phys. Rev. Lett, vol. 70, no. 15, pp. 2269-2272, 1993.
7. C. W. Gardiner and M. J. Collett, "Input and output in damped quantum systems: Quantum stochastic differential equations and the master equation", Phys. Rev. A, vol. 31, no. 6, pp. 3761-3774, 1985.
8. C. W. Gardiner and P. Zoller, Quantum Noise. Berlin, Germany: Springer, 2000.
9. J. Gough, "Holevo-ordering and the continuous-time limit for open floquet dynamics", Lett. Math. Phys., vol. 67, pp. 207-221, 2004. (Pubitemid 38945329)
10. J. Gough, "Quantum Stratonovich calculus and the quantum Wong-Zakai theorem", J. Math. Phys., vol. 47, p. 113509, 2006.
11. J. Gough and M. R. James, "Quantum feedback networks: Hamiltonian formulation", Commun. Math. Phys., vol. 287, no. 3, pp. 1109-1132, May 2008.
12. J. Gough, "Construction of bilinear control hamiltonians using the series product", Phys. Rev. A, vol. 78, p. 052311, 2008.
13. J. Gough, R. Gohm, and M. Yanagisawa, "Linear quantum feedback networks", Phys. Rev. A, vol. 78, p. 062104, 2008.
14. A. S. Holevo, "Time-ordered exponentials in quantum stochastic calculus", in Quantum Probability and Related Topics. London, U. K.: World Scientific, 1992, vol. 7, pp. 175-202.
15. R. L. Hudson and K. R. Parthasarathy, "Quantum Ito's formula and stochastic evolutions", Commun. Math. Phys, vol. 93, pp. 301-323, 1984.
16. M. R. James and J. Gough, "Quantum Dissipative Systems and Feedback Control Design by Interconnection", 2007 [Online]. Available: http://arxiv.org/abs/0707.1074
17. ∞control of linear quantum systems", IEEE Trans Autom. Control, vol. 53, no. 8, pp. 1787-1803, Sep. 2008.
18. S. Lloyd, "Coherent quantum feedback", Phys. Rev. A, vol. 62, p. 022108, 2000.
19. E. Merzbacher, Quantum Mechanics, 3 ed. New York: Wiley, 1998.
20. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge, U. K.: Cambridge Univ. Press, 2000.
21. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus. Berlin, Germany: Birkhauser, 1992.
22. R. v. Handel, J. Stockton, and H. Mabuchi, "Feedback control of quantum state reduction", IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 768-780, Jun. 2005. (Pubitemid 40902702)
23. P. Warszawski, H. M. Wiseman, and H. Mabuchi, "Quantum trajectories for realistic detection", Phys. Rev. A, vol. 65, p. 023802, 2002.
24. H. Wiseman, "Quantum theory of continuous feedback", Phys. Rev. A, vol. 49, no. 3, pp. 2133-2150, 1994.
25. H. M. Wiseman and G. J. Milburn, "All-optical versus electro-optical quantum-limited feedback", Phys. Rev. A, vol. 49, no. 5, pp. 4110-4125, 1994.
26. M. Yanagisawa and H. Kimura, "Transfer function approach to quantum control-part I: Dynamics of quantum feedback systems", IEEE Trans. Autom. Control, vol. 48, no. 12, pp. 2107-2120, Dec. 2003.
27. B. Yurke and J. S. Denker, "Quantum network theory", Phys. Rev. A, vol. 29, no. 3, pp. 1419-1437, 1984.