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Similarity analysis between quantum images

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Abstract

Similarity analyses between quantum images are so essential in quantum image processing that it provides fundamental research for the other fields, such as quantum image matching, quantum pattern recognition. In this paper, a quantum scheme based on a novel quantum image representation and quantum amplitude amplification algorithm is proposed. At the end of the paper, three examples and simulation experiments show that the measurement result must be 0 when two images are same, and the measurement result has high probability of being 1 when two images are different.

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References

  1. Venegas-Andraca, S.E., Ball, J.L.: Processing images in entangled quantum systems. Quantum Inf. Process. 9, 1–11 (2010)

    Article  MathSciNet  Google Scholar 

  2. Venegas-Andraca, S.E., Bose, S.: Storing, processing and retrieving an image using quantum mechanics. Quantum Inf. Comput. 5105, 137–147 (2003)

    ADS  Google Scholar 

  3. Latorre, J.I.: Image Compression and Entanglement. arXiv:quantph/0510031 (2005)

  4. Le, P.Q., Dong, F., Hirota, K.: A flexible representation of quantum images for polynomial preparation, image compression, and processing operations. Quantum Inf. Process. 10, 63–84 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zhang, Y., Lu, K., Gao, Y.H., Wang, M.: NEQR: a novel enhanced quantum representation of digital images. Quantum Inf. Process. 12, 2833–2860 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Zhang, Y., Lu, K., Gao, Y., Xu, K.: A novel quantum representation for log polar images. Quantum Inf. Process. 12, 3103–3126 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Le, P.Q., Iliyasu, A.M., Dong, F.Y., Hirota, K.: Fast geometric transformation on quantum images. IAENG Int. J. Appl. Math. 40, 113–123 (2010)

    MathSciNet  MATH  Google Scholar 

  8. Wang, J., Jiang, N., Wang, L.: Quantum image translation. Quantum Inf. Process. 14, 1589–1604 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Jiang, N., Wang, L.: Quantum image scaling using nearest neighbor interpolation. Quantum Inf. Process. 14, 1559–1571 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  10. Zhou, R.G., Hu, W., Ping, F., et al.: Quantum realization of the bilinear interpolation method for NEQR. Sci. Rep. 7, 2511 (2017)

    Article  ADS  Google Scholar 

  11. Zhou, R.G., Liu, X.A., Luo, J.: Quantum circuit realization of the bilinear interpolation method for GQIR. Int. J. Theor. Phys. 56, 2966–2980 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, H.S., Zhu, Q.X., Lan, S., Shen, C.Y., Zhou, R.G., Mo, J.: Image storage, retrieval, compression and segmentation in a quantum system. Quantum Inf. Process. 12, 2269–2290 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Caraiman, S., Manta, V.: Histogram-based segmentation of quantum images. Theor. Comput. Sci. 529, 46–60 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, Y., Lu, K., Xu, K., Gao, Y.H., Wilson, R.: Local feature point extraction for quantum images. Quantum Inf. Process. 14, 1573–1588 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Iliyasu, A.M., Le, P.Q., Dong, F., Hirota, K.: Watermarking and authentication of quantum images based on restricted geometric transformations. Inf. Sci. 186, 126–149 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang, W.W., Gao, F., Liu, B.: A watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12, 793–803 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Zhang, W.W., Gao, F., Liu, B.: A quantum watermark protocol. Int. J. Theory Phys. 52, 504–513 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang, Y.G., Jia, X., Xu, P., Tian, J.: Analysis and improvement of the watermark strategy for quantum images based on quantum Fourier transform. Quantum Inf. Process. 12, 2765–2769 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Song, X.H., Wang, S., Liu, S., El-Latif, A.A., Niu, X.M.: A dynamic watermarking scheme for quantum images using quantum wavelet transform. Quantum Inf. Process. 12, 3689–3706 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Song, X.H., Wang, S., Liu, S., El-Latif, A.A., Niu, X.M.: Dynamic watermarking scheme for quantum images based on Hadamard transform. Multimed. Syst. 20, 379–388 (2014)

    Article  Google Scholar 

  21. Jiang, N., Wang, L.: A quantum image information hiding algorithm based on Moiré pattern. Int. J. Theor. Phys. 54, 1021–1032 (2014)

    Article  Google Scholar 

  22. Jiang, N., Zhao, N., Wang, L.: LSB based quantum image steganography algorithm. Int. J. Theor. Phys. 55, 107–123 (2016)

    Article  MATH  Google Scholar 

  23. Yang, Y.G., Zhao, Q.Q., Sun, S.J.: Novel quantum gray-scale image matching. Optik 126, 3340–3343 (2015)

    Article  ADS  Google Scholar 

  24. Yan, F., et al.: Assessing the similarity of quantum images based on probability measurements. In: IEEE Evolutionary Computation, pp. 1–6 (2012)

  25. Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997)

    Article  ADS  Google Scholar 

  26. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)

  27. Boyer, M., Brassard, G., Høyer, P., et al.: Tight bounds on quantum searching. Fortschritteder Physik. 46, 493–505 (1996)

    Article  ADS  Google Scholar 

  28. Brassard, G., Høyer, P., Mosca, M., et al.: Quantum amplitude amplification and estimation. Quantum Comput. Inf. 5494, 53–74 (2000)

    MATH  Google Scholar 

  29. Jiang, N., Dang, Y., Wang, J.: Quantum image matching. Quantum Inf. Process. 15, 3543–3572 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61463016, “Science and technology innovation action plan” of Shanghai in 2017 under Grant No. 17510740300, and the advantages of scientific and technological innovation team of Nanchang City under Grant No. 2015CXTD003; H. I. acknowledges support by FDCT of Macau under Grant 065/2016/A2, University of Macau under Grant MYRG2014-00052-FST, and National Science Foundation of China under Grant 11404415.

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Zhou, RG., Liu, X., Zhu, C. et al. Similarity analysis between quantum images. Quantum Inf Process 17, 121 (2018). https://doi.org/10.1007/s11128-018-1894-x

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