Minimum-error discrimination between two sets of similarity-transformed quantum states

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• 作者：M. A. Jafarizadeh (1) (2) (3)
  Y. Mazhari Khiavi (1)
  Y. Akbari Kourbolagh (4)
  
• 关键词：Minimum error discrimination ; Similarity transformed quantum states ; Probability operator measure
• 刊名：Quantum Information Processing
• 出版年：2013
• 出版时间：July 2013
• 年：2013
• 卷：12
• 期：7
• 页码：2385-2404
• 全文大小：227KB
• 参考文献：1. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic, New York (1976)
  2. Holevo, A.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam (1982)
  3. Eldar, Y.C., Megretski, A., Verghese, G.C.: Designing optimal quantum detectors via semidefinite programming. IEEE Trans. Inf. Theory 49, 1007鈥?012 (2003) CrossRef
  4. Barnett, S.M., Croke, S.: On the conditions for discrimination between quantum states with minimum error. J. Phys. A Math. Theor. 42, 062001(4 pp) (2009)
  5. Barnett, S.M., Croke, S.: Quantum state discrimination. Adv. Opt. Photon. 1, 238鈥?78 (2009) CrossRef
  6. Jafarizadeh, M.A., Mazhari, Y., Aali, M.: The minimum-error discrimination via Helstrom family of ensembles and convex optimization. Quant. Inf. Process. 10, 155鈥?76 (2011) CrossRef
  7. Hwang, W.-Y., Bae, J.: Minimum-error state discrimination constrained by the no-signaling principle. J. Math. Phys. 51, 0222022 (11 pp) (2010)
  8. Assalini, A., Cariolaro, G., Pierobon, G.: Efficient optimal minimum error discrimination of symmetric quantum states. Phys. Rev. A 81, 012315 (4 pp) (2010) CrossRef
  9. Ivanovic, I.D.: How to differentiate between non-orthogonal states. Phys. Lett. A 123, 257鈥?59 (1987) CrossRef
  10. Dieks, D.: Overlap and distinguishability of quantum states. Phys. Lett. A 126, 303鈥?06 (1988) CrossRef
  11. Peres, A., Terno, D.R.: Optimal distinction between non-orthogonal quantum states. J. Phys. A 31, 7105鈥?112 (1998) CrossRef
  12. Jaeger, G., Shimony, A.: Optimal distinction between two non-orthogonal quantum states. Phys. Lett. A 197, 83鈥?7 (1995) CrossRef
  13. Chefles, A.: Unambiguous discrimination between linearly independent quantum states. Phys. Lett. A 239, 339鈥?47 (1998) CrossRef
  14. Jafarizadeh, M.A., Rezaei, M., Karimi, N., Amiri, A.R.: Optimal unambiguous discrimination of quantum states. Phys. Rev. A 77, 042314 (12 pp) (2008)
  15. Kimura, G., Miyadera, T., Imai, H.: Optimal state discrimination in general probabilistic theories. Phys. Rev. A 79, 062306 (9 pp) (2009)
  16. Jafarizadeh, M.A., Sufiani, R., Mazhari Khiavi, Y.: Minimum error discrimination between similarity-transformed quantum states. Phys. Rev. A 84, 012102 (9 pp) (2011)
  17. Joshi, A.W.: Elements of group theory for physicists. New Age International (P) Limited, Publishers, New Delhi (1997)
  18. James, G., Liebeck, M.W.: Representations and Characters of Groups. Cambridge University Press, NY (2001) CrossRef
  19. Andersson, E., Barnett, S.M., Gilson, C.R., Hunter, K.: Minimum-error discrimination between three mirror-symmetric states. Phys. Rev. A 65, 052308鈥? (2002) CrossRef
  20. Samsonov, B.F.: Minimum error discrimination problem for pure qubit states. Phys. Rev. A 80, 052305鈥?1 (2009) CrossRef
  21. Je啪ek, M., 艠eh谩膷ek, J., Fiur谩拧ek, J.: Finding optimal strategies for minimum-error quantum-state discrimination. Phys. Rev. A 65, 060301鈥? (2002) CrossRef
  22. Weinberg, S.: The Quantum Theory of Fields I. Cambridge University Press, NY (1995) CrossRef
  23. Jafarizadeh, M.A., Sufiani, R.: Bell-state diagonal entanglement witnesses for relativistic and nonrelativistic multispinor systems in arbitrary dimensions. Phys. Rev. A 77, 012105 (25 pp) (2008)
  
• 作者单位：M. A. Jafarizadeh (1) (2) (3)
  Y. Mazhari Khiavi (1)
  Y. Akbari Kourbolagh (4)
  
  1. Department of Theoretical Physics and Astrophysics, University of Tabriz, 51664, Tabriz, Iran
  2. Institute for Studies in Theoretical Physics and Mathematics, 19395-1795, Tehran, Iran
  3. Research Institute for Fundamental Sciences, 51664, Tabriz, Iran
  4. Department of Physics, Azarbaijan University of Tarbiat Moallem, 53714-161, Tabriz, Iran
  
• ISSN：1573-1332

文摘

Using the equality form of the necessary and sufficient conditions introduced in Jafarizadeh (Phys Rev A 84:012102 (9 pp), 2011), minimum error discrimination between states of the two sets of equiprobable similarity transformed quantum qudit states is investigated. In the case that the unitary operators describing the similarity transformations are generating sets of two irreducible representations and the states fulfill a certain constraint, the optimal set of measurements and the corresponding maximum success probability of discrimination are determined in closed form. In the cases that they are generating sets of reducible representations, there exist no closed-form formula in general, but the procedure can be applied properly in each case provided that the states obey some constraints. Finally, we give the maximum success probability of discrimination and optimal measurement operators for some important examples of mixed quantum states, such as generalized Bloch sphere m-qubit states, qubit states and their three special cases.