Home | About Journal | Web Links | E-mail Alerts | RSS RSS Icon | Browse
Previous Article Next Article

Minimum-error state discrimination constrained by the no-signaling principle

Source: J. Math. Phys. 51, 022202 (2010); doi:10.1063/1.3298647

Published 8 February 2010

KEYWORDS and PACS
Keywords
PACS
  • 03.65.Ta
    Foundations of quantum mechanics; measurement theory
  • 03.67.-a
    Quantum information
  • YEAR: 2010
RELATED DATABASES

To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.
PUBLICATION DATA
Publisher:
AIP is a member of CrossRef AIP
Won-Young Hwang1 and Joonwoo Bae2
1Department of Physics Education, Chonnam National University, Gwangju 500-757, Republic of Korea
2School of Computational Sciences, Korea Institute for Advanced Study, Seoul 130-012, Republic of Korea
We provide a bound on the minimum error when discriminating among quantum states, using the no-signaling principle. The bound is general in that it depends on neither dimensions nor specific structures of given quantum states to be discriminated among. We show that the bound is tight for the minimum-error state discrimination between symmetric (both pure and mixed) qubit states. Moreover, the bound can be applied to a set of quantum states for which the minimum-error state discrimination is not known yet. Finally, our results strengthen the quantitative connection between two no-go theorems, the no-signaling principle, and the no perfect state estimation. ©2010 American Institute of Physics
History: Received 8 October 2009; accepted 29 December 2009; published 8 February 2010
Permalink: http://link.aip.org/link/?JMAPAQ/51/022202/1

REFERENCES (28)

For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. N. Gisin, Phys. Lett. A 242, 1 (1998).
  2. S. M. Barnett and E. Andersson, Phys. Rev. A 65, 044307 (2002).
  3. W. -Y. Hwang, Phys. Rev. A 71, 062315 (2005).
  4. J. Bae, J. Lee, J. Kim, and W. -Y. Hwang, Phys. Rev. A 78, 022335 (2008).
  5. S. Croke, E. Andersson, and S. M. Barnett, Phys. Rev. A 77, 012113 (2008).
  6. A. Montanaro, Proceedings of the IEEE Information Theory Workshop, 2008 (unpublished), p. 378
    7. e-print arXiv:0711.2012.
  7. J. Tyson, J. Math. Phys. 50, 032106 (2009)
    8. J. Tyson, e-print arXiv:0907.3386.
  8. D. Qiu, Phys. Rev. A 77, 012328 (2008).
  9. D. Qiu and L. Li, e-print arXiv:0812.2378.
  10. C. Helstrom, Quantum Detection and Estimation Theory (Academic, New York, 1976).
  11. Y. C. Eldar and G. D. Forney, IEEE Trans. Inf. Theory 47, 858 (2001).
  12. U. Herzog, Fortschr. Phys. 49, 981 (2001).
  13. M. Ježek, J. Rehacek, and J. Fiurasek, Phys. Rev. A 65, 060301 (2002).
  14. H. P. Yuen, R. S. Kennedy, and M. Lax, IEEE Trans. Inf. Theory 21, 125 (1975).
  15. A. S. Holevo, J. Multivariate Anal. 3, 337 (1973).
  16. A. S. Holevo, Probl. Inf. Transm. 10, 51 (1974).
  17. Ll. Masanes, A. Acín, and N. Gisin, Phys. Rev. A 73, 012112 (2006).
  18. J. S. Bell, Physics 1, 195 (1964).
  19. For instance, no-cloning theorem, D. Dieks, Phys. Lett. 92A, 271 (1982)
    20. W. K. Wootters and W. H. Zurek, Nature (London) 299, 802 (1982)
    H. P. Yuen, Phys. Lett. 113A, 405 (1986).
  20. J. Bae and A. Acín, Phys. Rev. Lett. 97, 030402 (2006).
  21. N. Gisin, Helv. Phys. Acta 62, 363 (1989).
  22. L. P. Hughston, R. Jozsa, and W. K. Wootters, Phys. Lett. A 183, 14 (1993).
  23. In the case that the probability is obtained by measuring quantum states, the probability P(k|rhol) can be expressed with POVMs, {mk} that discriminates among {rhok}, [summation]kmk=I, where each mk concludes that the state rhok is detected: P(k|rhol)=tr[mkrhol].
  24. The value p can be computed by taking the two identical ensembles rhoB,i and rhoB,j in (21) with i[not-equal]j. It follows from the fact that rhoB,i=rhoB,j, that (1−p)(deltaj−deltai)=p(rhoi−rhoj). One can then apply the trace norm, denoted by ||·||, and obtain the following relation: p=||deltai−deltaj||/(||deltai−deltaj||+||rhoi−rhoj||). Note that the trace norm is defined as, ||A||=trsqrt(A[sup [dagger]]A), or equivalently, ||A||=[summation]j|lambdaj|, where lambdaj are eigenvalues of A. It is then explicitly computed in (22).
  25. C. -L. Chou and L. Y. Hsu, Phys. Rev. A 68, 042305 (2003).
  26. H. -P. Breuer, Phys. Rev. A 71, 062330 (2005).
  27. G. Kimura, T. Miyadera, and H. Imai, Phys. Rev. A 79, 062306 (2009).
  28. R. Konig, R. Renner, and C. Schaffner, IEEE Trans. Inf. Theory 55, 4337 (2009).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.
ADVERTISEMENT