Analytical expression for variance of homogeneous-position quantum walk with decoherent position
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We have derived an analytical expression for variance of homogeneous-position decoherent quantum walk with general form of noise on its position, and have shown that, while the quadratic (\(t^2\)) term of variance never changes by position decoherency, the linear term (t) does and always increases the variance. We study the walker with ability to tunnel out to d nearest neighbors as an example and compare our result with former studies. We also show that, although our expression has been derived for asymptotic case, the rapid decay of time-dependent terms causes the expressions to be correct with a good accuracy even after dozens of steps.
KeywordsQuantum walk Decoherency Variance Coin-position entanglement
I would sincerely like to thank Maryam Boozarjmehr from the Australian National University, for her accurate reading and editing the manuscript.
- 11.Kempe, J.: Quantum random walks hit exponentially faster. In: Proceedings of 7th International Workshop on Randomization and Approximation Techniques in Computer Science (RANDOM’03), pp. 354–69 (2003)Google Scholar
- 14.Kendon, V., Tregenna, B.: Decoherence in discrete quantum walks. In: Decoherence and Entropy in Complex Systems. Lecture Notes in Physics, vol. 633, pp. 253–267. Springer, Berlin (2003)Google Scholar
- 18.Nayak, A., Vishwanath, A.: Quantum walk on a line, DIMACS Technical Report 2000-43 (2001)Google Scholar
- 26.Venegas-Andraca, S.E., Bose, S.: Quantum walk-based generation of entanglement between two walkers (2009). arXiv:0901.3946