Analytical expression for variance of homogeneous-position quantum walk with decoherent position
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.
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