Quantum stochastic differential equations and continuous measurements: Unbounded coefficients

Reports on Mathematical Physics

Volumn 67, Issue 2, 2011, Pages 229-254

  Santis, Ricardo Castro ^a   Barchielli, Alberto ^b  

^a UNIVERSIDAD DEL BÍO BÍO   (Chile)

^b POLITECNICO DI MILANO   (Italy)

Author keywords

Degenerate parametric oscillator; Quantum continuous measurements; Quantum dynamical semigroups with unbounded generator; Quantum stochastic calculus

Indexed keywords

EID: 80052517405     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0034-4877(11)80014-5     Document Type: Article

References (27)

1. Accardi L. On the quantum Feynman-Kac formula. Rend. Sem. Mat. Fis. Milano 1978, XLVIII.
2. Barchielli A. Stochastic processes and continual measurements in quantum mechanics. Stochastic Processes in Classical and Quantum Systems, Lecture Notes in Physics 262 1986, 14-23. Springer, Berlin. S. Albeverio, G. Casati, D. Merlini (Eds.).
3. Barchielli A. Measurement theory and stochastic differential equations in quantum mechanics. Phys. Rev. A 1986, 34:1642-1649.
4. Barchielli A. Direct and heterodyne detection and other applications of quantum stochastic calculus to quantum optics. Quantum Opt. 1990, 2:423-441.
5. Barchielli A. Continual Measurements in Quantum Mechanics and Quantum Stochastic Calculus. Open Quantum Systems III, Lecture Notes in Mathematics 1882 2006, 207-291. Springer, Berlin. S. Attal, A. Joye, C.-A. Pillet (Eds.).
6. Barchielli A., Gregoratti M. Quantum Trajectories and Mesurements in Continuous Time, Lecture Notes in Physics 782 2009, Springer, Berlin.
7. Barchielli A., Lupieri G. Quantum stochastic calculus, operation valued stochastic processes and continual measurements in quantum mechanics. J. Math. Phys. 1985, 26:2222-2230.
8. Belavkin V.P. Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processes. Modelling and Control of Systems 1988, Springer, Berlin, Lecture Notes in Control and Information Sciences 121. A. Blaquière (Ed.).
9. Belavkin V.P. Measurement, Filtering and Control in Quantum Open Dynamical Systems. Rep. Math. Phys. 1999, 43:405-425.
10. Bottero C. A Qualitative Analysis of two Master Equations in Quantum Optics. PhD thesis 2008, Department of Mathematics, Politecnico di Milano.
11. Carmichael H.J. Statistical Methods in Quantum Optics 2. Non-Classical Fields 2008, Springer, Berlin.
12. Castro Santis R. Quantum Stochastic Calculus and Continual Measurements: The case of Unbounded Coefficients. PhD thesis January 2007, Department of Mathematics, Univesità di Roma La Sapienza.
13. Fagnola F. Quantum Markov Semigroups and Quantum Flows, Proyecciones. Journal of Mathematics 1999, 18(no. 3).
14. Fagnola F. H-P Quantum stochastic differential equations. Quantum Probability and White Noise Analysis 2002, World Sci., River Edge, NJ, QPPQ, XVI, 5196. N. Obata, T. Matsui, A. Hora (Eds.).
15. Fagnola F. Quantum stochastic differential equations and dilation of completely positive semigroups. Open Quantum Systems II, Lecture Notes in Mathematics 1881 2006, 183-220. Springer, Berlin. S. Attal, A. Joye, C.-A. Pillet (Eds.).
16. Fagnola F., Wills S.J. Solving quantum stochastic differential equations with unbounded coefficients. J. Funct. Anal. 2003, 198:279-310.
17. Frigerio A. Covariant Markov dilations of quantum dynamical semigroups. Pub. RIMS Kyoto Univ. 1985, 21:657-675.
18. Gardiner C.W., Zoller P. Quantum Noise 2000, Springer, Berlin.
19. Grangier P., Slusher R.E., Yurke B., La Porta A. Squeezed-lightenhanced polarization interferometer. Phys. Rev. Lett. 1987, 59.
20. Hudson R.L., Parthasarathy K.R. Quantum ItÔ's formula and stochastic evolutions. Commun. Math Phys. 1984, 93:301-323.
21. Parthasarathy K.R. An Introduction to Quantum Stochastic Calculus 1992, Birkhäuser, Basel.
22. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations 1983, Springer, Berlin.
23. Reed M., Simon B. Methods of Modern Mathematical Physics: I Functional Analysis 1980, Academic Press.
24. Sakai S. C*-Algebras and W*-Algebras 1971, Springer, Berlin.
25. Zoller P., Gardiner C.W. Quantum noise in quantum optics: the stochastic Schrödinger equation. Fluctuations quantiques (Les Mouches 1995) 1997, 79-136. North-Holland, Amsterdam. S. Reynaud, E. Giacobino, J. Zinn-Justin (Eds.).
26. Wu L.-A., Kimble H.J., Hall J.L., Wu H. Generation of squeezed states by parametric down conversion. Phys. Rev. Lett. 1986, 57:2520-2523.
27. Wu L.-A., Xiao M., Kimble H.J. Squeezed states of light from an optical parametric oscillator. J. Opt. Soc. Am. B 1987, 4:1465-1475.