On the separation principle in quantum control

Quantum Stochastics and Information: Statistics, Filtering, and Control

Volumn , Issue , 2008, Pages 206-238

  Bouten, Luc ^a   Van Handely, Ramon ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Controlled quantum ow; Quantum ltering; Quantum stochastic control; Separation theorem

Indexed keywords

EID: 84969631067     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812832962_0010     Document Type: Chapter

References (31)

1. V. P. Belavkin, Autom. Remote Control 44, 178 (1983).
2. V. P. Belavkin, Nondemolition stochastic calculus in Fock space and nonlinear filtering and control in quantum systems, in Proceedings XXIV Karpacz winter school, eds. R. Guelerak and W. Karwowski (World Scientific, 1988).
3. M. A. Armen, J. K. Au, J. K. Stockton, A. C. Doherty and H. Mabuchi, Phys. Rev. Lett. 89, p. 133-602 (2002).
4. J. M. Geremia, J. K. Stockton and H. Mabuchi, Science 304, 270 (2004).
5. R. L. Hudson and K. R. Parthasarathy, Comm. Math. Phys. 93, 301 (1984).
6. V. P. Belavkin, J. Multivar. Anal. 42, 171 (1992).
7. L. Bouten, M. I. Guta and H. Maassen, J. Phys. A 37, 3189 (2004).
8. L. Bouten and R. Van Handel, Quantum filtering: a reference probability approach (2005), preprint, arXiv:math-ph/0508006.
9. R. Van Handel, J. K. Stockton and H. Mabuchi, IEEE Trans. Automat. Control 50, 768 (2005).
10. M. Mirrahimi and R. Van Handel, Stabilizing feedback controls for quantum systems (2005), SIAM J. Control Optim., at press, arXiv:quant-ph/0510066.
11. M. Zakai, Z. Wahrsch. th. verw. Geb. 11, 230 (1969).
12. W. M. Wonham, SIAM J. Control 6, 312 (1968).
13. A. Segall, IEEE Trans. Automat. Control AC-22, 179 (1977).
14. L. Bouten and R. Van Handel, Controlled quantum stochastic processes (2007), in preparation.
15. M. Takesaki, J. Funct. Anal. 9, 306 (1971).
16. P. Biane, Calcul stochastique noncommutatif, in Lectures on Probability Theory, Saint-Flour, 1993, ed. P. Bernard, Lecture Notes in Mathematics, Vol. 1608 (Springer, 1995).
17. P.-A. Meyer, Quantum Probability for Probabilists (Springer, 1993).
18. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus (Birkhauser, 1992).
19. A. S. Holevo, J. Soviet Math. 56, 2609 (1991)
20. Translation of Itogi Nauki i Tekhniki, ser. sovr. prob. mat. 36, 3-28, 1990.
21. S. Holevo, Proc. Roy. Soc. Edinburgh Sect. A 126, 375 (1996).
22. D. Goswami, J. M. Lindsay and S. J. Wills, Math. Ann. 319, 647 (2001).
23. L. Bouten, Filtering and control in quantum optics (2004), Ph.D. thesis.
24. H. M. Wiseman, Phys. Rev. Lett. 75, 4587 (1995).
25. R. S. Liptser and A. N. Shiryaev, Statistics of Random Processes I: General Theory, second edn. (Springer, 2001).
26. P. E. Protter, Stochastic Integration and Differential Equations, second edn. (Springer, 2004).
27. H. Kushner, Introduction to stochastic control (Holt Rinehart Winston, 1971).
28. A. Sulem, Applied stochastic control of jump diffusions (Springer, 2005).
29. M. R. James, J. Opt. B Quantum Semiclass. Opt. 7, S198 (2005).
30. K. R. Parthasarathy and K. B. Sinha, Probab. Th. Rel. Fields 75, 317 (1987).
31. R. Van Handel, Stopping times in quantum control (2006), in preparation.