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

Abstract

We have derived an analytical expression for variance of homogeneous-position decoherent quantum walk (HPDQW) 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 have been derived for asymptotic case, the rapid decay of time-dependent terms cause the expressions to be correct with a good accuracy even after dozens of steps.

Asymptotic reduced density matrix of discrete-time quantum walks

“…At the end we should emphasize that, this method can be useful for investigating other asymptotic properties, which does not have direct connection to the reduced density matrix. For example, we have shown that the modified form of RDCM can be used to obtain the general form of 'limiting distribution' in quantum walk on cycle (our study is under review [31]) or long-time variance which has been studied previously by super operator method [32,33] or direct calculation in Fourier space [34] can be derived by modified version of RDCM. In fact, we have found a bidirectional map between RDCM and super-operator method (this study is on progress).…”

Entanglement production by the magnetic dipolar interaction dynamics

“…Besides, the MDI was used to simulate spin systems [14] and to obtain an Ising interaction [15] from which CNOT gates (an essential ingredient for universal quantum computation [16]) can be implemented. Due to the creation of quantum correlations between system and environment [17,18], which leads to the classicality of the first, the MDI is the source of noise is several physical systems [19][20][21][22][23][24][25]. So it is important, from the fundamental and practical points of view, to investigate the dynamics of quantum coherence and of quantum correlations due to the MDI.…”