Skip to main content

Statistical inference for quantum processes

  • Session III: Quantum Stochastic Processes
  • Conference paper
  • First Online:
Quantum Aspects of Optical Communications

Part of the book series: Lecture Notes in Physics ((LNP,volume 378))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Davies E.B. Quantum theory of open system. — London: AP, 1976.

    Google Scholar 

  2. Holevo A.S. Probabilistic and statistical aspects of quantum theory. — Amsterdam: North Holland, 9-1982.

    Google Scholar 

  3. Kraus K. States, effects and operations//LNP — 1983 — v. 190.

    Google Scholar 

  4. Helstrom C.W. Quantum detection and estimation theory.-New York. AP, — 1976.

    Google Scholar 

  5. Holevo A.S. Covariant measurements and imprimitivity systems. In: Quantum probability and applications to the quantum theory of irreducible processes (ed. L.Accardi, A.Frigerio, V.Gorini)// LNP-Berlin: Springer-Verlag — 1984-v. 1055.-p. 163–172.

    Google Scholar 

  6. Ozawa M. Conditional probability and a posteriori states in quantum mechanics //Publ. RIMS-1985-v. 21, N 2.-p. 279–295.

    Google Scholar 

  7. Ozawa M. Quantum measuring processes of continuous observables // J. Math. Phys. — 1984 — v. 25.-p. 79–87.

    Google Scholar 

  8. Barchielli A., Lanz L., Prosperi G.M. A model for macroscopic description and continuous observations in quantum mechanics //Nuovo Cimento.-1982.-v. 72B-p. 79–121.

    Google Scholar 

  9. Holevo A.S. Conditionally positive definite functions in quantum probability //Proc. Intern. Congr. of Math., Berkeley, Calif. USA, 1986.–1987.-p. 1011–1020.

    Google Scholar 

  10. Srinivas M.D., Davies E.B. Opt. Acta-1981-v. 28-p. 981–996.

    Google Scholar 

  11. Holevo A.S. Quantum probabilistic study of counting statistics with application to the “Dolinar receiver” //Izv. vuzov. M atematika.-1982-v. 8-p. 3–19 (Russian).

    Google Scholar 

  12. Hudson R.L., Parthasarathy K.R. Quantum Ito's formula and stochastic evolutions //Commun. Math. Phys.-1984.-v. 93, N 3.-P. 301–323.

    Google Scholar 

  13. Gardiner C.W., Collet M.J. Input and output in damped quantum systems: quantum statistical differential equations and the master equation //Phys. Rev.-1985.-A31.-p. 3761–3774.

    Google Scholar 

  14. Barchielli A., Lupieri G. Dilations of operation-valued stochastic processes. In: Quantum probability and applications II (ed. L.Accardi, W. von Waldenfels) // LNM-1985-v. 1136-p. 57–66.

    Google Scholar 

  15. Holevo A.S. Quantum stochastic calculus. In: VINITI. Itogi nauki i techniki. ser. Sovr. probl. mat. v. 36-1990-P. 3–28 (Russian).

    Google Scholar 

  16. Liptzer R.S., Shiryaev A.N. Statistics. of random processes.-Moscow, Nauka.-1974 (Russian.).

    Google Scholar 

  17. Belavkin V.P. Nonlinear filtering of quantum continuous signal. In: 9th All-Union conference on coding theory and information transmission. Abstracts. v. 2-Odessa-1988-P. 342–345. (Russian).

    Google Scholar 

  18. Belavkin V.P. In: Stochastic methods in mathematics and physics. Proc. 24 Karpacz winter school on theoretical physics. (ed. R.Gielerak and W.Karwowski)-Singapore: World Scientific.-1989-p. 310.

    Google Scholar 

  19. Chirardi G., Rimini A., Weber T. A model for unified quantum description of macroscopic and microscopic system. In: Quantum probability and applications II (ed. L.Accardi, W. von Waldenfels) //LNM-Berlin: Springer-Verlag-1985-v. 1136-p. 223–233.

    Google Scholar 

  20. Gisin N. Stochastic quantum dynamics and relativity //Helv. Phys. Acta-1989-v. 62-p. 363–371.

    Google Scholar 

  21. Chirardi G., Pearle P., Rimini A. Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles //Preprint ICTP. IC/89/44-1989.

    Google Scholar 

  22. Gatarek D., Gisin N. Continuous quantum jumps and infinitedimensional stochastic equation //Preprint Université de Genève-1990.

    Google Scholar 

  23. Barchielli A., Belavkin V.P. Measurement continuous in time and a posteriori states in quantum mechanics //Preprint IFUM 383/FT-1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Cherif Bendjaballah Osamu Hirota Serge Reynaud

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Holevo, A. (1991). Statistical inference for quantum processes. In: Bendjaballah, C., Hirota, O., Reynaud, S. (eds) Quantum Aspects of Optical Communications. Lecture Notes in Physics, vol 378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53862-3_174

Download citation

  • DOI: https://doi.org/10.1007/3-540-53862-3_174

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53862-2

  • Online ISBN: 978-3-540-46366-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics