Related papers: Controlling quantum walks with coin eigenstates
We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time…
We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its…
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform…
We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators are built to exhibit a random inhomogeneity…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
In this study we show a way of achieving the reverse evolution of n-dimensional quantum walks by introducing interventions on the coin degree of freedom during the forward progression of the coin-walker system. Only a single intervention is…
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits…
We propose a scheme for perfect transfer of an unknown qubit state via the discrete-time quantum walk on a line or a circle. For this purpose, we introduce an additional coin operator which is applied at the end of the walk. This operator…
While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a…
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and…
In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the…
The conditional shift in the evolution operator of a quantum walk generates entanglement between the coin and position degrees of freedom. This entanglement can be quantified by the von Neumann entropy of the reduced density operator…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle which depends upon the position of a quantum particle parameterizes the coin operator. For different values…
A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is…
We consider an special dynamics of a quantum walk (QW) on a line. Initially, the walker localized at the origin of the line with arbitrary chirality, evolves to an asymptotic stationary state. In this stationary state a measurement is…
We propose a new model for a measurement of a characteristic of a microscopic quantum state by a large system that selects stochastically the different eigenstates with appropriate quantum weights. Unlike previous works which formulate a…
Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…
One-parameter family of discrete-time quantum-walk models on the square lattice, which includes the Grover-walk model as a special case, is analytically studied. Convergence in the long-time limit $t \to \infty$ of all joint moments of two…