A note on a formula of the Lévy-Khinchin type in quantum probability

Nagoya Mathematical Journal

Volumn 141, Issue , 1996, Pages 29-43

  Barchielli, A ^a   Paganoni, A M ^a  

^a UNIVERSITY OF MILAN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030093742     PISSN: 00277630     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0027763000005511     Document Type: Article

References (20)

1. V. P. Belavkin Nondemolition measurements, nonlinear filtering and dynamic programming of quantum stochastic processes, In A. Blaquiere (ed.), Modelling and Control of Systems, Lecture Notes in Control and Information Sciences, vol.121, Springer, Berlin, 1988, pp.245-265.
2. L. Diósi, Continuous quantum measurement and Ito formalism, Phys. Lett. A129 (1988), 419-423.
3. A. Barchielli, V. P. Belavkin, Measurements continuous in time and a posteriori states in quantum mechanics, J. Phys. A: Math. Gen., 24 (1991), 1495-1514.
4. A. Barchielli, Stochastic differential equations and 'a posteriori' states in quantum mechanics, Int. J. Theor. Phys., 32 (1993), 2221-2232.
5. A. Barchielli, On the quantum theory of measurements continuous in time, Rep. Math. Phys., 33 (1993), 21-34.
6. V. P. Belavkin, P. Staszewski, A continuous observation of photon emission, Rep. Math. Phys., 29 (1991), 213-225.
7. A. Barchielli, Some stochastic differential equations in quantum optics and measurement theory: the case of counting processses. In L. Diósi, B. Lukács (ed.), Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, World Scientific, Singapore, 1994, pp.1-14.
8. H. J. Carmichael, An Open System Approach to Quantum Optics, Lect. Notes in Physics, Series m, vol. 18, Springer, Berlin, 1993.
9. H. M. Wiseman, G. J. Milburn, Interpretation of quantum jump and diffusion processes illustrated on the Bloch sphere, Phys. Rev. A, 47 (1993), 1652-1666.
10. N. Gisin, P. L. Knight, I. C. Percival, R. C. Thompson, D. C. Wilson, Quantum state diffusion theory and a quantum jump experiment, J. Mod. Opt., 40 (1993), 1663-1671.
11. A. Barchielli, A. S. Holevo, Constructing quantum measurement processes via classical stochastic calculus, Stochastic Processes and their Applications, 58 (1995) 293-317.
12. A. Barchielli, Probability operators and convolution semigroups of instruments in quantum probability, Probab. Theory Rel. Fields, 82 (1989), 1-8.
13. A. Barchielli, G. Lupieri, A quantum analogue of Hunt's representation theorem for the generator of convolution semigroups on Lie groups, Probab. Theory Rel. Fields, 88 (1991), 167-194.
14. A. Barchielli, A. S. Holevo, G. Lupieri, An analogue of Hunt's representation theorem in quantum probability, J. Theor. Probab., 6 (1993), 231-265.
15. E. B. Davies, Quantum Theory of Open Systems, Academic Press, London, 1976.
16. S. Sakai, C*-algebras, Springer, Berlin, 1971.
17. W. Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966.
18. G. Lindblad, On the generators of quantum dynamical semigroups. Commun. Math. Phys., 48 (1976), 119-130.
19. M. Ozawa, Quantum measuring processes of continuous observables, J. Math. Phys., 25 (1984), 79-87.
20. M. Reed, B. Simon, Methods of Modern Mathematical Physics. I: Functional Analysis, Academic, New York, 1972.