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A quantum random walk on the integers exhibits pseudo memory effects, in thatits probability distribution after N steps is determined by reshuffling thefirst N distributions that arise in a classical random walk with the sameinitial distribution. In a classical walk, entropy increase can be regarded asa consequence of the majorization ordering of successive distributions. TheLorenz curves of successive distributions for a symmetric quantum walk revealno majorization ordering in general. Nevertheless, entropy can increase, andcomputer experiments show that it does so on average. Varying the stages atwhich the quantum coin system is traced out leads to new quantum walks,including a symmetric walk for which majorization ordering is valid but thespreading rate exceeds that of the usual symmetric quantum walk.Comment: 3 figures include

Pseudo memory effects, majorization and entropy in quantum random walks