ﻻ يوجد ملخص باللغة العربية
The analysis of a physical problem simplifies considerably when one uses a suitable coordinate system. We apply this approach to the discrete-time quantum walks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wigner walks), a model which was introduced in T. Miyazaki et al., Phys. Rev. A 76, 012332 (2007). First, we show that from the three parameters of the coin operator only one is physically relevant for the limit density of the Wigner walk. Next, we construct a suitable basis of the coin space in which the limit density of the Wigner walk acquires a much simpler form. This allows us to identify various dynamical regimes which are otherwise hidden in the standard basis description. As an example, we show that it is possible to find an initial state which reduces the number of peaks in the probability distribution from generic $2j+1$ to a single one. Moreover, the models with integer $j$ lead to the trapping effect. The derived formula for the trapping probability reveals that it can be highly asymmetric and it deviates from purely exponential decay. Explicit results are given up to the dimension five.
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain range of dynam
Chirally symmetric discrete-time quantum walks possess supersymmetry, and their Witten indices can be naturally defined. The Witten index gives a lower bound for the number of topologically protected bound states. The purpose of this paper is to give
We study one-dimensional quantum walk with four internal degrees of freedom resulted from two entangled qubits. We will demonstrate that the entanglement between the qubits and its corresponding coin operator enable one to steer the walkers state fro
One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, albeit the system is translationally invariant. The effect is dependent on the d
One of the earliest cryptographic applications of quantum information was to create quantum digital cash that could not be counterfeited. In this paper, we describe a new type of quantum money: quantum coins, where all coins of the same denomination