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Analysis of the two-particle controlled interacting quantum walks

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Abstract

We have recently proposed the two-particle controlled interacting quantum walks for building quantum Hash schemes (Li et al. Quantum Inf Proc, 2012. doi:10.1007/s11128-012-0421-8). In this paper, we adopt the mutual information, the measurement-induced disturbance and the quantum mutual information to measure the classical correlation, the quantum correlation and the total correlation between two particles respectively. Our conclusion is that the correlation between the particles of the two-particle controlled interacting quantum walks is similar to that of the two-particle interacting quantum walks. It is superb for keeping the quantum Hash scheme safe.

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References

  1. Li, D. et al.: Discrete-time interacting quantum walks and quantum Hash schemes. Quantum Inf. Proc. (2012). doi:10.1007/s11128-012-0421-8

  2. Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)

    Article  ADS  Google Scholar 

  3. Berry, S.D., Wang, J.B.: Two-particle quantum walks: entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011)

    Article  ADS  Google Scholar 

  4. Chandrashekar, C.M.: Zeno subspace in quantum-walk dynamics. Phys. Rev. A 82, 052108 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  5. \(\text{ G}\ddot{o}\text{ n}\ddot{u}\)lol, M., Aydiner, E., Shikano, Y., \(\text{ M}\ddot{u}\)stecaplio\(\tilde{g}\)lu, \(\ddot{O}\).E.,: Survival probability in a one-dimensional quantum walk on a trapped lattice. New J. Phys. 13, 033037 (2011)

  6. Franco, C.D., Gettrick, M.M., Busch, Th: Mimicking the probability distribution of a two-dimensional Grover walk with a single-qubit coin. Phys. Rev. Lett. 106, 080502 (2011)

    Article  Google Scholar 

  7. Franco, C.D., Gettrick, M.M., Machida, T., Busch, Th: Alternate two-dimensional quantum walk with a single-qubit coin. Phys. Rev. A 84, 042337 (2011)

    Article  ADS  Google Scholar 

  8. \(\check{S}\text{ tefa}\check{n}\acute{a}\)k, M., Barnett, S.M., Koll\(\acute{a}\)r, B., Kiss, T., Jex, I.: Directional correlations in quantum walks with two particles. New J. Phys. 13, 033029 (2011)

  9. Xue, P., Sanders, B.C.: Two quantum walkers sharing coins. Phys. Rev. A 85, 022307 (2012)

    Article  ADS  Google Scholar 

  10. Omar, Y.: Paunkovi\(\acute{c}\), N., Sheridan, L., Bose, S.: Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006)

    Google Scholar 

  11. Pathak, P.K., Agarwal, G.S.: Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75, 032351 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  12. Banuls, M.C., Navarrete, C.: P\(\acute{e}\)rez, A., Rold\(\acute{a}\)n, E., Soriano, J.C.: Quantum walk with a time-dependent coin. Phys. Rev. A 73, 062304 (2006)

  13. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)

    Article  ADS  Google Scholar 

  14. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008)

    Article  ADS  Google Scholar 

  15. Brodutch, A., Terno, D.R.: Quantum discord, local operations, and Maxwell’s demons. Phys. Rev. A 81, 062103 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  16. Rao, B.R., Srikanth, R., Chandrashekar, C.M., Banerjee, S.: Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord. Phys. Rev. A 83, 064302 (2011)

    Article  ADS  Google Scholar 

  17. Cavalcanti, D., Aolita, L., Boixo, S., Modi, K., Piani, M., Winter, A.: Operational interpretations of quantum discord. Phys. Rev. A 83, 032324 (2011)

    Article  ADS  Google Scholar 

  18. Dakić, B., Vedral, V., Brukner, C.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)

    Article  ADS  Google Scholar 

  19. Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2008)

    Article  ADS  Google Scholar 

  20. Modi, K., Paterek, T., Son, W., Vedral, V., Williamson, M.: Unified view of quantum and classical correlations. Phys. Rev. Lett. 104, 080501 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  21. Li, N., Luo, S.: Total versus quantum correlations in quantum states. Phys. Rev. A 76, 032327 (2007)

    Article  ADS  Google Scholar 

  22. Srikanth, R., Banerjee, S., Chandrashekar, C.M.: Quantumness in a decoherent quantum walk using measurement-induced disturbance. Phys. Rev. A 81, 062123 (2010)

    Article  ADS  Google Scholar 

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Acknowledgments

This work is supported by NSFC (Grant Nos. 61170270, 61100203, 60903152, 61003286, 61121061), NCET (Grant No. NCET-10-0260), SRFDP (Grant No. 20090005110010), Beijing Natural Science Foundation (Grant Nos. 4112040, 4122054), the Fundamental Research Funds for the Central Universities (Grant Nos. BUPT2011YB01, BUPT2011RC0505, 2011PTB-00-29, 2011RCZJ15, 2012RC0612).

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Authors and Affiliations

  1. State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Dan Li, Jie Zhang, Xiu-Wen Ma, Wei-Wei Zhang & Qiao-Yan Wen

  2. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Dan Li & Jie Zhang

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  1. Dan Li
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  2. Jie Zhang
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Correspondence to Dan Li.

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Li, D., Zhang, J., Ma, XW. et al. Analysis of the two-particle controlled interacting quantum walks. Quantum Inf Process 12, 2167–2176 (2013). https://doi.org/10.1007/s11128-012-0516-2

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