Infinite reduction in absorbing time in quantum walks over classical ones
Harish-Chandra Research Institute, A CI of Homi Bhabha National Institute（哈里什-昌德拉研究所，霍米·巴哈国家学院下属机构）；National Institute of Technology Agartala（阿加塔拉国立技术学院）
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of the quantum walker is finite, contrary to the behavior of a classical random walker, indicating an infinite resource reduction on moving over to a quantum version of a walker. Furthermore, numerical simulations indicate a reversal of this behavior due to the insertion of disorder in the walker's step lengths. Additionally, we demonstrate that in the presence of an absorber, there is a speed-up in the spreading rate, and that a disordered quantum walk that is sub-ballistic regains the ballistic spreading of a clean quantum walk.
Dipartimento Interuniversitario di Fisica, Università di Bari（巴里大学跨学科物理系）；INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）；Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague（布拉格捷克理工大学核科学与物理工程学院物理系）
A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks
Recent work on recurrence in quantum walks has provided a representation of Schur functions in terms of unitary operators . We propose a generalization of Schur functions by extending this operator representation to arbitrary operators on Banach spaces . Such generalized Schur functions meet the formal structure of first return generating functions, thus we call them FR-functions. We derive general properties of FR-functions, among them a generalization of the renewal equation already known for random and quantum walks, as well as splitting properties which extend useful factorizations of Schu…
