TY  - JOUR
AU  - Hinarejos, M.
AU  - Di Franco, C.
AU  - Romanelli, A.
AU  - Perez, A.
PY  - 2014
DA  - 2014//
TI  - Chirality asymptotic behavior and non-Markovianity in quantum walks on a line
T2  - Phys. Rev. A
JO  - Physical Review A
SP  - 052330
EP  - 7pp
VL  - 89
IS  - 5
PB  - Amer Physical Soc
AB  - We investigate the time evolution of the chirality reduced density matrix for a discrete-time quantum walk on a one-dimensional lattice. The matrix is obtained by tracing out the spatial degree of freedom. We analyze the standard case, without decoherence, and the situation in which decoherence appears in the form of broken links in the lattice. By examining the trace distance for possible pairs of initial states as a function of time, we conclude that the evolution of the reduced density matrix is non-Markovian, in the sense defined by Breuer, Laine, and Piilo [Phys. Rev. Lett. 103, 210401 (2009)]. As the level of noise increases, the dynamics approaches a Markovian process. The highest non-Markovianity corresponds to the case without decoherence. The reduced density matrix tends always to a well-defined limit that we calculate, but only in the decoherence-free case is this limit nontrivial.
SN  - 1050-2947
UR  - http://arxiv.org/abs/1401.3243
UR  - https://doi.org/10.1103/PhysRevA.89.052330
DO  - 10.1103/PhysRevA.89.052330
LA  - English
N1  - WOS:000336751300003
ID  - Hinarejos_etal2014
ER  -