Advertisement

Quantum Information Processing

, Volume 1, Issue 1–2, pp 73–89 | Cite as

How Do Two Observers Pool Their Knowledge About a Quantum System?

  • Kurt Jacobs
Article

Abstract

In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine independently obtained states of knowledge together to form a new state of knowledge, which is the state which would be possessed by someone having the combined information of both observers. Moreover, this combined state of knowledge can be found without reference to the manner in which the respective observers obtained their information. However, we show that in general this is not possible for quantum states of knowledge; in order to combine two quantum states of knowledge to obtain the state resulting from the combined information of both observers, these observers must also possess information about how their respective states of knowledge were obtained. Nevertheless, we emphasize this does not preclude the possibility that a unique, well motivated rule for combining quantum states of knowledge without reference to a measurement history could be found. We examine both the direct quantum analog of the classical problem, and that of quantum state-estimation, which corresponds to a variant in which the observers share a specific kind of prior information.

PACS: 03.67.-a, 02.50.-r, 03.65.Bz

quantum mechanics quantum information Bayesian inference state estimation states of knowledge 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    E. T. Jaynes, in Papers on Probability, Statistics, and Statistical Physics, ed. by R. D. Rosenkrantz, (Dordrecht, Holland, 1983).Google Scholar
  2. 2.
    T. Bayes, Phil. Trans. Roy. Soc. 330 (1763); or see, e.g., S. J.Press, Bayesian Statistics: Principles, Models, and Applications (Wiley, New York, 1989).Google Scholar
  3. 3.
    T. A. Brun, J. Finkelstein, and N. D. Mermin, quant-ph/0109041.Google Scholar
  4. 4.
    K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory, Lecture Notes in Physics Vol. 190 (Springer Verlag, Berlin, 1983); B. Schumacher, Phys. Rev. A 54, 2614 (1996), Eprint: quant-ph/9604023.Google Scholar
  5. 5.
    K. R. W Jones, Phys. Rev. A 50, 3682 (1994).Google Scholar
  6. 6.
    S. Massar and S. Popescu, Phys. Rev. Lett. 74 1259 (1995).Google Scholar
  7. 7.
    Z. Hradil, Phys. Rev. A 55, R1561 (1997).Google Scholar
  8. 8.
    P. B. Slater, J. Math. Phys. 38, 2274 (1997).Google Scholar
  9. 9.
    R. Derka, V. Buzek, and A.K. Ekert, Phys. Rev. Lett. 80, 1571 (1998).Google Scholar
  10. 10.
    V. Buzek, R. Derka, G. Adam, and P. L. Knight, Ann. Phys. (N.Y.) 266, 454 (1998).Google Scholar
  11. 11.
    R. Tarrach and G. Vidal, Phys. Rev. A 60, 3339 (1999).Google Scholar
  12. 12.
    K. Banaszek, G. M. D'Ariano, M. G. A Paris, and M. F. Sacchi, Phys. Rev. A 61, 10304 (2000).Google Scholar
  13. 13.
    R. D. Gill and S. Massar, Phys. Rev. A 61, 42312 (2000).Google Scholar
  14. 14.
    R. Schack, T. A. Brun, and C. M. Caves, Phys. Rev. A 64, 014305 (2001).Google Scholar
  15. 15.
    C. M. Caves, C. A. Fuchs, and R. Schack, Eprint: quant-ph/0104088.Google Scholar
  16. 16.
    I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • Kurt Jacobs
    • 1
  1. 1.T-8, Theoretical Division, MS B285Los Alamos National LaboratoryLos Alamos

Personalised recommendations