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Optimal unambiguous discrimination of pure qudits

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Abstract

Linearly independent pure quantum states can be discriminated unambiguously, while linearly dependent states cannot. We use a physical accessible unitary transformation to map the nonorthogonal quantum states onto a set of orthogonal ones so that measuring the output states can discriminate the initial states with the deterministic and inconclusive results. The failure states that give an inconclusive result are linearly dependent ones. In finding the optimal unambiguous discrimination (UD), we show that a main constraint condition that the determinant constructed by the complex inner products of the failure states must be zero, along with two additional conditions, can provide solutions to the problem of the optimal UD for pure qudits. For any d, we give one analytical solution as all the Berry phases being zero. We also derive the lowest bound of the total failure probability of the optimal UD.

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References

  1. Gisin, N., Ribordy, G., Tittel, W., et al.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  2. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N., et al.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009)

    Article  ADS  Google Scholar 

  3. Barnett, S.M., Croke, S.: Quantum state discrimination. Adv. Opt. Photon. 1, 238 (2009)

    Google Scholar 

  4. Bergou, J.A.: Discrimination of quantum states J. Mod. Opt. 57, 160 (2010)

    Google Scholar 

  5. Chefles, A.: Unambiguous discrimination between linearly independent quantum states. Phys. Lett. A 239, 339 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Ivanovic, I.D.: How to differentiate between non-orthogonal states. Phys. Lett. A 123, 257 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  7. Dieks, D.: Overlap and distinguishability of quantum states. Phys. Lett. A 126, 303 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  8. Peres, A.: How to differentiate between non-orthogonal states. Phys. Lett. A 128, 19 (1988)

    Article  MathSciNet  ADS  Google Scholar 

  9. Jaeger, G., Shimony, A.: Optimal distinction between two non-orthogonal quantum states. Phys. Lett. A 197, 83 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Terno, D.R.: Optimal distinction between non-orthogonal quantum states. J. Phys. A 31, 7105 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Clarke, R.B.M., Chefles, A., Barnett, S.M., et al.: Experimental demonstration of optimal unambiguous state discrimination. Phys. Rev. A 63, 040305(R) (2001)

    Article  ADS  Google Scholar 

  12. Sun, Y., Hillery, M., Bergou, J.A.: Optimum unambiguous discrimination between linearly independent nonorthogonal quantum states and its optical realization. Phys. Rev. A 64, 022311 (2001)

    Article  ADS  Google Scholar 

  13. Jafarizadeh, M.A., Rezaei, M., Karimi, N., et al.: Optimal unambiguous discrimination of quantum states. Phys. Rev. A 77, 042314 (2008)

    Article  ADS  Google Scholar 

  14. Herzog, U., Bergou, J.A.: Optimum unambiguous identification of d unknown pure qudit states. Phys. Rev. A 78, 032320 (2008)

    Article  ADS  Google Scholar 

  15. Pang, S., Wu, S.: Optimum unambiguous discrimination of linearly independent pure states. Phys. Rev. A 80, 052320 (2009)

    Article  ADS  Google Scholar 

  16. Sugimoto, H., Hashimoto, T., Horibe, M., et al.: Complete solution for unambiguous discrimination of three pure states with real inner products. Phys. Rev. A 82, 032338 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  17. Bergou, J.A., Futschik, U., Feldman, E.: Optimal unambiguous discrimination of pure quantum states. Phys. Rev. Lett. 108, 250502 (2012)

    Article  ADS  Google Scholar 

  18. Zhou, X.-F., Lin, Q., Zhang, Y.-S., et al.: Physical accessible transformations on a finite number of quantum states. Phys. Rev. A 75, 012321 (2007)

    Article  ADS  Google Scholar 

  19. Zhou, X.-F., Zhang, Y.-S., Guo, G.-C.: Unambiguous discrimination of mixed states: a description based on system–ancilla coupling. Phys. Rev. A 75, 052314 (2007)

    Article  ADS  Google Scholar 

  20. Chen, P.-X., Bergou, J.A., Zhu, S.-Y., et al.: Ancilla dimensions needed to carry out positive-operator-valued measurement. Phys. Rev. A 76, 060303 (R) (2007)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

This research was funded by the National Science Foundation of China under Grants No. 11074002, No. 61073048, and No. 11104057, and the Natural Science Foundation of the Education Department of Anhui Province of China under Grants No. KJ2010ZD08 and No. KJ2012A245, and the Postgraduate Program of Huainan Normal University.

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Authors and Affiliations

  1. Department of Physics, Huainan Normal University, Huainan, 232001, People’s Republic of China

    Wen-Hai Zhang

  2. School of Electronic and Information Engineering, Hefei Normal University, Hefei, 230061, People’s Republic of China

    Long-Bao Yu & Zhuo-Liang Cao

  3. School of Physics and Material Science, Anhui University, Hefei, 230039, People’s Republic of China

    Liu Ye

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  1. Wen-Hai Zhang
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  2. Long-Bao Yu
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  3. Zhuo-Liang Cao
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  4. Liu Ye
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Correspondence to Wen-Hai Zhang.

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Zhang, WH., Yu, LB., Cao, ZL. et al. Optimal unambiguous discrimination of pure qudits. Quantum Inf Process 13, 503–511 (2014). https://doi.org/10.1007/s11128-013-0666-x

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  • DOI: https://doi.org/10.1007/s11128-013-0666-x

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