Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2015, Article ID 683658, 5 pages
http://dx.doi.org/10.1155/2015/683658
Research Article

Entropic Lower Bound for Distinguishability of Quantum States

1Center for Macroscopic Quantum Control, Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Republic of Korea
2Department of Physics, Hanyang University, Seoul 133-791, Republic of Korea

Received 18 August 2015; Accepted 22 October 2015

Academic Editor: Remi Léandre

Copyright © 2015 Seungho Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, New York, NY, USA, 1976.
  2. A. S. Holevo, Statistical Structure of Quantum Theory, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  3. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, “The security of practical quantum key distribution,” Reviews of Modern Physics, vol. 81, no. 3, pp. 1301–1350, 2009. View at Publisher · View at Google Scholar · View at Scopus
  4. S. M. Barnett and S. Croke, “Quantum state discrimination,” Advances in Optics and Photonics, vol. 1, no. 2, pp. 238–278, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. K. M. R. Audenaert, J. Calsamiglia, R. Muñoz-Tapia et al., “Discriminating states: the quantum Chernoff bound,” Physical Review Letters, vol. 98, no. 16, Article ID 160501, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. J. A. Bergou and M. Hillery, “Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states,” Physical Review Letters, vol. 94, no. 16, Article ID 160501, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Dušek and V. Bužek, “Quantum-controlled measurement device for quantum-state discrimination,” Physical Review A, vol. 66, no. 2, Article ID 022112, 2002. View at Google Scholar · View at Scopus
  8. M. Hayashi, A. Kawachi, and H. Kobayashi, “Quantum measurements for hidden subgroup problems with optimal sample complexity,” Quantum Information and Computation, vol. 8, no. 3-4, pp. 0345–0358, 2008. View at Google Scholar
  9. A. Montanaro, “A lower bound on the probability of error in quantum state discrimination,” in Proceedings of the IEEE Information Theory Workshop (ITW '08), pp. 378–380, Porto, Portugal, May 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Qiu, “Minimum-error discrimination between mixed quantum states,” Physical Review A, vol. 77, Article ID 012328, 2008. View at Google Scholar
  11. D. Qiu and L. Li, “Minimum-error discrimination of quantum states: bounds and comparisons,” Physical Review A, vol. 81, no. 4, Article ID 042329, 2010. View at Publisher · View at Google Scholar
  12. J. Tyson, “Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds,” Journal of Mathematical Physics, vol. 50, no. 3, Article ID 032106, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. S. Kholevo, “On asymptotically optimal hypothesis testing in quantum statistics,” Theory of Probability & Its Applications, vol. 23, no. 2, pp. 411–415, 1979. View at Publisher · View at Google Scholar
  14. A. Montanaro, “On the distinguishability of random quantum states,” Communications in Mathematical Physics, vol. 273, no. 3, pp. 619–636, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. H. Barnum and E. Knill, “Reversing quantum dynamics with near-optimal quantum and classical fidelity,” Journal of Mathematical Physics, vol. 43, no. 5, pp. 2097–2106, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. B. Schumacher, “Quantum coding,” Physical Review A, vol. 51, no. 4, pp. 2738–2747, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. Jozsa and J. Schlienz, “Distinguishability of states and von Neumann entropy,” Physical Review. A, vol. 62, no. 1, Article ID 012301, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  18. A. Nayak and J. Salzman, “Limits on the ability of quantum states to convey classical messages,” Journal of the ACM, vol. 53, no. 1, pp. 184–206, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. C. Adami and N. J. Cerf, “von Neumann capacity of noisy quantum channels,” Physical Review A, vol. 56, no. 5, pp. 3470–3483, 1997. View at Publisher · View at Google Scholar · View at Scopus
  20. R. Renner and S. Wolf, “Smooth rényi entropy and applications,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT '04), p. 232, July 2004. View at Scopus
  21. R. Koenig, R. Renner, and C. Schaffner, “The operational meaning of min- and max-entropy,” IEEE Transactions on Information Theory, vol. 55, no. 9, pp. 4337–4347, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. M. Tomamichel, R. Colbeck, and R. Renner, “A fully quantum asymptotic equipartition property,” IEEE Transactions on Information Theory, vol. 55, no. 12, pp. 5840–5847, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. L. Henderson and V. Vedral, “Classical, quantum and total correlations,” Journal of Physics. A. Mathematical and General, vol. 34, no. 35, pp. 6899–6905, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. B. Groisman, S. Popescu, and A. Winter, “Quantum, classical, and total amount of correlations in a quantum state,” Physical Review. A, vol. 72, no. 3, Article ID 032317, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. A. S. Holevo, “Statistical problems in quantum physics,” in Proceedings of the Second Japan-USSR Symposium on Probability Theory, G. Maruyama and J. V. Prokhorov, Eds., vol. 330 of Lecture Notes in Mathematics, pp. 104–119, Springer, Berlin, Germany, 1973. View at Publisher · View at Google Scholar
  26. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, UK, 2000. View at MathSciNet
  27. H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Physical Review Letters, vol. 88, no. 1, Article ID 017901, 2001. View at Publisher · View at Google Scholar
  28. J. Bae, “Structure of minimum-error quantum state discrimination,” New Journal of Physics, vol. 15, Article ID 073037, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus