Skip to main content
Log in

On the simultaneous measurement of spin components using spin-1/2 meters: Naimark embedding and projections

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

Measurements involving spin-1/2 meters which result in the simultaneous measurement of spin components are described. The spin analoge of the Arthur-Kelly experiment is contrasted with a simultaneous measurement which interacts with the system. Naimark extensions are constructed and Bloch state projection properties are discussed for each case. The theory is extended to squeezed angular momentum measurement.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. E. Arthurs and J. L. Kelly, Jr.,Bell Sys. Tech. J. 44, 725, (1965).

    Google Scholar 

  2. C. W. Helstrom,Quantum Detection and Estimation Theory, (Academic Press, New York, 1976), p. 141.

    Google Scholar 

  3. M. A. Naimark,Izv. Akad. Nauk. SSSR, Ser. Mat. 4, 227, (1940);C.R. Acad. Sci. URSS 41, 359, (1943).

    Google Scholar 

  4. C. W. Helstrom,Int. J. Theor. Phys. 8, 361, (1973).

    Google Scholar 

  5. R. Y. Levine and R. R. Tucci,Found. Phys. 19, (1989).

  6. H. P. Yuen,Phys. Lett. 91A, 101, (1982); C. Y. She and H. Heffner,Phys. Rev. 152, 1103, (1966).

    Google Scholar 

  7. H. P. Yuen,Phys. Rev. A13, 2226, (1976).

    Google Scholar 

  8. Y. Yamamoto, N. Imoto, and S. Machida,Phys. Rev. A33, 3243, (1986); H. A. Haus and Y. Yamamoto,Phys. Rev. A34, 270, (1986).

    Google Scholar 

  9. Y. Yamamoto and H. A. Haus,Rev. Mod. Phys. 58, 1001, (1986).

    Google Scholar 

  10. C. Aragone, G. Guerri, S. Salamo, and J. L. Tani,J. Phys. A7, L149, (1974); C. Aragone, E. Chalbaud, and S. Salamo,J. Math. Phys. 17, 1963, (1976).

  11. J. M. Radcliffe,J. Phys. A4, 313, (1971); F. T. Arrechi, E. Courtens, R. Gilmore, and H. Thomas,Phys. Rev. A6, 2211, (1972), and references therein.

    Google Scholar 

  12. A. M. Perelomov,Comm. Math. Phys. 26, 222, (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Levine, R.Y., Tucci, R.R. On the simultaneous measurement of spin components using spin-1/2 meters: Naimark embedding and projections. Found Phys 19, 175–187 (1989). https://doi.org/10.1007/BF00734524

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00734524

Keywords

Navigation