Decoherence in two-dimensional quantum walks with two- and four-state coins
Abstract
Two-dimensional quantum walks using a two-state coin have simpler experimental implementation than two-dimensional quantum walks using a four-state coin. However, decoherence occurs inevitably during the evolution of quantum walks due to the coupling between the quantum systems and their environment. Thus, it is interesting to investigate the robustness against decoherence for two- and four-state two-dimensional quantum walks. Here, we investigate the effects of the decoherence on two- and four-state two-dimensional quantum walks produced by the broken-link-type noise and compare their robustness against the broken-link-type noise. Specifically, we analyze the quantum correlation between the two spatial dimensions x and y by using measurement-induced disturbance for the two-state quantum walks, i.e. the alternate walk and the Pauli walk, and the four-state quantum walks, i.e. the Grover, Hadamard and Fourier walks, respectively. Our analysis shows that the two-state walks are more robust against the broken-link-type noise than the four-state walks.
References
- 1. , SIGACT News 35, 22 (2004). Google Scholar
- 2. , Proc. 45th Annual IEEE Symp. Foundations of Computer Science (FOCS’04)
(2004) , pp. 22–31. Google Scholar - 3. , Phys. Rev. Lett. 102, 180501 (2009). ISI, ADS, Google Scholar
- 4. , Phys. Rev. A 81, 042330 (2010). ISI, ADS, Google Scholar
- 5. , Phys. Rev. A 82, 042304 (2010). ISI, ADS, Google Scholar
- 6. , Phys. Rev. A 78, 022314 (2008). ISI, ADS, Google Scholar
- 7. , Phys. Rev. A 83, 022320 (2011). ISI, ADS, Google Scholar
- 8. , Phys. Rev. A 82, 033429 (2010). ISI, ADS, Google Scholar
- 9. , J. Phys. A: Math. Theor. 43, 235303 (2010). ISI, ADS, Google Scholar
- 10. , Phys. Rev. A 67, 042316 (2003). ISI, ADS, Google Scholar
- 11. , Phys. Rev. A 72, 062317 (2005). ISI, ADS, Google Scholar
- 12. , Phys. Rev. A 81, 022308 (2010). ISI, ADS, Google Scholar
- 13. , Phys. Rev. Lett. 103, 090504 (2009). ISI, ADS, Google Scholar
- 14. , Phys. Rev. Lett. 104, 100503 (2010). ISI, ADS, Google Scholar
- 15. , Phys. Rev. Lett. 104, 153602 (2010). ISI, ADS, Google Scholar
- 16. , Science 329, 1500 (2010). ISI, ADS, Google Scholar
- 17. , Phys. Rev. Lett. 106, 180403 (2011). ISI, ADS, Google Scholar
- 18. , Phys. Rev. Lett. 108, 010502 (2012). ISI, ADS, Google Scholar
- 19. , Science 325, 174 (2009). ISI, ADS, Google Scholar
- 20. , Phys. Rev. A 48, 1687 (1993). ISI, ADS, Google Scholar
- 21. , Phys. Rev. A 58, 915 (1998). ISI, ADS, Google Scholar
- 22. , Phys. A 338, 395 (2004). ISI, Google Scholar
- 23. , Quantum Inf. Process. 1, 345 (2002). ISI, Google Scholar
- 24. , New J. Phys. 7, 221 (2005). ISI, Google Scholar
- 25. , Quantum Potential Theory,
Lecture Notes in Mathematics , Vol. 1954 (Springer-Verlag, 2008), p. 309. Google Scholar - 26. , Quantum Walks for Computer Scientists (Morgan and Claypool, 2008). Google Scholar
- 27. , Phys. Lett. A 317, 21 (2003). ISI, ADS, Google Scholar
- 28. , Int. J. Quantum. Inform. 5, 781 (2007). Link, ISI, Google Scholar
- 29. , J. Phys. A 35, 2745 (2002). ADS, Google Scholar
- 30. , New J. Phys. 7, 156 (2005). ISI, Google Scholar
- 31. , Phys. Rev. A 74, 042304 (2006). ISI, ADS, Google Scholar
- 32. , Phys. Rev. A 77, 062331 (2008). ISI, ADS, Google Scholar
- 33. , Proc. 6th Int. Workshop on Randomization and Approximation Techniques (RANDOM 2002),
Lecture Notes in Computer Science , Vol. 2483, eds. J. D. P. RolimS. Vadhan (Springer-Verlag, 2002), pp. 164–178. Google Scholar - 34. , Phys. Rev. A 77, 042312 (2008). ISI, ADS, Google Scholar
- 35. , Phys. Rev. A 67, 042315 (2003). ISI, ADS, Google Scholar
- 36. , Int. J. Quantum Inf. 1, 51 (2003). Link, ISI, Google Scholar
- 37. , J. Chem. Phys. 129, 174106 (2008). ISI, ADS, Google Scholar
- 38. , Phys. Rev. A 67, 032304 (2003). ISI, ADS, Google Scholar
- 39. , Phys. A 347c, 137 (2005). ISI, ADS, Google Scholar
- 40. , Phys. Rev. A 79, 032319 (2009). ISI, ADS, Google Scholar
- 41. , Phys. Rev. A 77, 022301 (2008). ISI, ADS, Google Scholar
- 42. , Phys. Rev. Lett. 106, 180403 (2011). ISI, ADS, Google Scholar
- 43. , J. Math. Phys. 52, 042201 (2011). ISI, Google Scholar
- 44. , Phys. Rev. A 86, 025601 (2012). ISI, ADS, Google Scholar
- 45. , New J. Phys. 16, 123052 (2014). ISI, Google Scholar
- 46. , Phys. Rev. A 94, 062317 (2016). ISI, ADS, Google Scholar
- 47. , Phys. Rev. Lett. 106, 080502 (2011). ISI, ADS, Google Scholar
- 48. , Phys. Rev. A 84, 042337 (2011). ISI, ADS, Google Scholar
- 49. , Phys. Rev. A 81, 062340 (2010). ISI, ADS, Google Scholar
- 50. C. M. Chandrashekar, arXiv:1103.2704. Google Scholar
- 51. , J. Phys. A: Math. Theor. 46, 105306 (2013). ISI, ADS, Google Scholar
- 52. , Phys. Rev. A 74, 012312 (2006). ISI, ADS, Google Scholar
- 53. , New J. Phys. 5, 83 (2003). ISI, Google Scholar
- 54. , Phys. Rev. Lett. 88, 017901 (2001). ISI, ADS, Google Scholar
- 55. , Phys. Rev. A 83, 064302 (2011). ISI, ADS, Google Scholar
- 56. , Int. J. Theor. Phys. 59, 436 (2020). ISI, Google Scholar
- 57. , Quantum Inf. Process. 20, 128 (2021). ISI, ADS, Google Scholar
- 58. , Int. J. Theor. Phys. 60, 1374 (2021). ISI, Google Scholar
- 59. , Int. J. Theor. Phys. 60, 1237 (2021). ISI, Google Scholar
- 60. , Int. J. Theor. Phys. 59, 1442 (2020). ISI, Google Scholar
- 61. , Mod. Phys. Lett. B 34, 2050172 (2020). Link, ISI, ADS, Google Scholar
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